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ISAAC  NEWTON  MATL1CK,  A.  M. 


HAND     BOOK 


TO     THE 


itatltrk  5te  lUtriatt 


GUIDE  TO    MATHEMATICAL 
AND  ASTRONOMICAL  GEOGRAPHY 


—BY— 


ISAAC     NEWTON     MATLICK.    A.    M. 


PUBLISHED     BY 

AMERICAN    TELLURIAN    MFG.    Co 
SEATTLE       TAEuLL5GmAANM      WASH. 

AGENCIES  IN   PRINCIPAL    CITIES  IN   U.  S. 


AND   IN   FOREIGN    COUNTRIES 


Copyrighted  by 
The   American   Tellurian   Co. 
1915. 

Press  of 

MECHANICS  PUBLISHING  COMPANY 
Seattle,  Wash.,  U.  S.  A. 


Isaac  Newton  Matlick,  A.  M. 


Isaac  Newton  Matlick,  inventor  of  the  tel- 
lurian which  bears  his  name,  was  born  in 
Pleasant  Township,  West  Virginia,  in  the  year 
1846;  and  died  in  San  Francisco,  California, 
February  the  third,  1913:  His  remains  being 
interred  in  Lone  Fir  Cemetery,  Portland,  Ore- 
gon. It  was  in  this  city  where  Prof.  Matlick 
served  many  years  as  a  principal  'of  schools 
that  he  brought  to  completion  the  invention  of 
his  tellurian.  iTo  this  great  task  he  gave 
thirty-one  years  of  painstaking  effort.  The 
achievement  should  give  him  rank  among  the 
great  mathematicians  and  mechanics  of  the 
world. 

Those  who  knew  him  testify  to  his  great 
strength  of  character,  combined  with  kind- 
liness of  heart  and  fine  humility.  His  inven- 
tion, wonderful  in  its  capacity  to  make  plain 
the  great  laws  of  the  world  and  the  solar 
system,  should  make  his  name  familiar  to  the 
youth  of  many  generations. 


PSALM  XIX. 


The  Heavens  declare  the  glory  of  God 

And  the  firmament  showeth  His  handiwork. 

Day  unto  day  uttereth  speech 

And  night  unto  night  showeth  knowledge. 

There  is  no  speech  nor  language; 

Their  voice  is  not  heard ; 

Their  line  is  gone  out  through  all  the  Earth 

And  their  words  to  the  end  of  the  World. 

In  them  hath  He  set  a  tabernacle  for  the  Sun 

Which  is  as  a  bridegroom  coming  out  of  his 

chamber 
And   rejoiceth   as   a   strong  man   to   run    His 

course. 
His    going    forth    is    from    the    end    of    the 

Heavens, 

And  His  circuit  unto  the  ends  of  it, 
And    there    is    nothing    hid    from    the    heat 

thereof. 

Psalms  XIX,  vs.  1-6. 


Table  of  Contents 


Page 

Isaac  Newton  Matlick,  A.  M 6 

Introduction     11 

Description   of   the   Tellurian .  15 

The    Earth     19 

Change   of    Seasons    34 

The    Moon     45 

The    Tides     67 

Time     78 

Precession  of  the  Equinoxes   ......  81 

The   Solar   System 85 

Glossary  of  Technical  Terms 88 

How  to  Set  up  and  Adjust  the  Tellurian. 96 

How  to  Demonstrate  to  a  Class  What  the  Axis  of 

the   Earth   Means    .                                                     .  97 


List  of  Illustrations 


Plate  Page 
Frontispiece  3 

II.  The  Tellurian  Insert 

[II.  The  Moon  44 

IV.  Eclipse  of  the  Sun  57 

V.     Precession   of   the   Equinoxes ,...,..,.    §3 


Diagrams 


Fig.  Page 

1.     Illustrating   Kepler's  Second   Law 26 

2 48 

3 48 

4 49 

5 49 

6 48 

7 55 

8 55 

9.                                       ^..,,.,..r^. 56 


Introduction 


This  Hand-book  is  designed  as,  a  guWe  to  the 
Teacher  or  Student  m,  using  .Matlick's  New 
Tellurian.  In  the  preparation  of  this  work  we 
have  endeavored  to  present  the  principal  points 
to  be  shown  by  the  Tellurian,  in  a  plain,  simple 
manner,  so  that  the  inexperienced  Teacher,  as 
well  as  the  Pupil,  may  readily  comprehend 
them.  There  are  many  'other  points  that  the 
thoughtful  Teacher  will  find  valuable  to  present 
which  can  be  accurately  explained  with  the 
Tellurian. 

The  Tellurian  represents  accurately,  in  the 
most  simple  mianner,  the  intricate  and  complex 
movements  of  the  Earth  and  Moon  around  the 
Sun,  showing  their  relative  positions  to  each 
other  any  day  of  the  year,  so  that  the  following 
points  may  be  readily  comprehended: 

1.  The  causes  of  a  change  of  season. 

2.  The  causes  of  day  and  night,  and  of  the 

variations  in  length  of  day  and  night 
in  different  latitudes. 

3.  The  portion  of  the  Earth  illuminated 

each  day  in  the  year. 


—12— 

4.  The  point  on  the  Earth  where  the  direct 

rays  of  the  Sun  will  shine  each  day  of 
the  year. 

5.  The  cause  of  the  difference  in  length  of 

;  days  or  nights, 

6.  The  inclination  of  the  Earth's  equator 

and  axis  to  the  plane  of  the  ecliptic. 

7.  The  direction  of  the  Sun's  rays  to  the 

surface  of  the  Earth  at  different 
seasons  of  the  year,  and  at  any  hour 
in  the  day. 

8.  Causes    of    the    present    shape    of    the 

Earth. 

9.  The  nature  and  causes  of  trade  winds. 

10.  The  Sun's  declinations. 

11.  Causes    and   phenomena   of   the   Equi- 

noxes. 

12.  Nutations  of  the  Earth's  polar  axis. 

13.  The     difference     between     solar     and 

siderial  time. 

14.  The    difference    between    siderial    and 

clock  time. 

15.  Causes  of  the  Sun  being  slow  or  fast. 

16.  How  mean  time  is  computed. 

17.  The  extent  and  duration  of  twilight  on 

any  part  of  the  Earth. 

18.  The  different  phases  of  the  Moon. 

19.  Causes    of   annular,   partial    and   total 

eclipses  of  the  Sun. 

20.  Eclipses  of  the  Moon. 


—13— 

21.  Umbra  and  penumbra. 

22.  The  Moon's  nodes  and  their  revolution. 

23.  Eevolution  of  the  apsides. 

24.  Causes  and  phenomena  of  the  tides- 

spring  and  neap  tides. 

25.  Effects    of    perigee    and    apogee    upon 

eclipses  and  tides. 

26.  The  siderial  and  lunar  month. 

27.  Comparative    size    of    the    Earth    and 

Moon. 

28.  Center   of   gravity   of   the    Earth   and 

Moon. 

29.  Causes  of  the  harvest  Moon. 

The  following  geographical  and  astronomical 
terms  can  also  be  illustrated,  viz. :  Latitude, 
longitude,  meridians,  palallels,  axis,  poles, 
tropics,  polar  circles,  zenith  and  nadir,  vertical 
circles,  celestial  meridian,  prime  vertical, 
azimuth,  etc. 

In  this  Hand-book  the  phenomena  of  the 
tides  are  explained  on  a  different  hypothesis 
from  that  generally  given  in  text-books ;  a  com- 
prehension of  the  lunar  motion  of  the  Earth, 
which  is  represented  by  the  Tellurian,  being 
necessary  to  explain  the  subject. 

Thus  it  will  be  readily  seen  that  it  is  not  only 
a  necessity,  but  an  indispensable  apparatus  for 
the  Public  School,  and  valuable  for  High 
Schools  and  Colleges,  where  the  more  intricate 
problems  are  to  be  studied,  as  it  is  impossible 


—14— 

for  any  Teacher,  however  apt  in  illustration,  or 
concise  in  language,  to  present  clearly  to  the 
mind  of  the  pupil  the  above  points  without  the 
aid  of  proper  apparatus.  As  such  apparatus, 
it  is  conceded  by  the  leading  educators  that 
the  Matlick  Tellurian  has  no  equal. 

Although  heretofore,  for  the  want  of  proper 
apparatus,  these  subjects  have  been  imper- 
fectly understood,  it  is  now  certain  that,  in  the 
imimediate  future,  they  will  be  properly  ex- 
plained in  every  school-room  through  the  use 
of  this  marvelously  complete  and  accurate  in- 
strument. 


Description  of  the  Tellurian 


The  top  of  the  stand  (Plate  1)  is  elliptical  to 
represent  the  ellipticity  of  the  Earth's  orbit. 
The  periphery  is  made  to  represent  the 
zodiacal  belt — a  belt  16°  in  width  with  the 
ecliptic  as  its  center. 

Upon  the  center  of  the  stand  is  a  revolving 
hub  having  a  socket  (No.  7)  into  which  is 
placed  the  Earth-arm,  (No.  3)  which  is  held  in 
place  by  a  set-screw  (No.  8).  At  the  outer  end 
of  the  Earth-arm,  driven  by  a  bevel  gear,  is  a 
vertical  shaft  which  by  a  simple  mechanism 
carries  the  globe  made  to  represent  the  Earth, 
and  also  the  Moon-arm-cam  (No.  10).  Upon 
the  Moon-arm  (No.  4)  is  placed  the  Moon 
which  is  constructed  upon  the  same  scale  as  the 
Earth.  The  Earth  is  supplied  with  a  time 
band  (No.  13),  a  day-band  (No.  16),  and  an 
adjustable  meridian  (No.  17). 

As  the  vertical  shaft  is  rotated  the  Earth  and 
Moon  revolve  about  their  common  center  of 
gravity,  the  Earth  maintaining  its  proper  in- 
clination to  the  plane  of  the  ecliptic,  the  North 
Pole  being  always  directed  to  the  same  objec- 
tive point,  thus  showing  very  clearly  the  third 


—16— 

or  lunar  motion  of  the  Earth.  The  Moon  rises 
and  falls  in  its  orbit  and  passes  through  all  its 
phases,  showing  the  inclination  of  its  orbit  to 
the  ecliptic  and  the  gyration  of  its  nodes,  which 
are  so  arranged  that  not  only  the  cause  but  the 
date  of  recurring  eclipses  may  be  shown  by  the 
Tellurian. 

The  day-band  shows  the  exact  portion  of  the 
Earth  illuminated  by  the  Sun  each  day  in  the 
year.  With  the  day-band,  time-band  and  ad- 
justable meridian  a  child  of  ten  can  tell  the 
time  of  sunrise  and  of  sunset  for  any  place  and 
date.  The  degree  of  latitude  on  the  Earth  im- 
mediately under  the  noon  point  of  the  time- 
band  will  indicate  the  distance  of  the  vertical 
rays  of  the  Sun  north  or  south  of  the  Equator 
for  each  day  in  the  year. 

The  mechanism  may  be  thrown  out  of  gear 
by  releasing  the  clutch  (No.  12)  by  means  of 
the  thumb-screw.  When  released  the  Earth 
may  be  revolved  on  its  orbit  without  rotating 
on  its  axis ;  or  the  Earth  and  Moon  may  be  re- 
volved about  their  common  center  of  gravity 
without  moving  the  Earth  along  its  orbit.  The 
axis  rod  (No.  14)  is  rotated  by  simple  friction 
so  that  the  Earth  may  be  rotated  on  its  axis 
without  moving  any  other  parts. 

The  top  and  periphery  of  the  stand  is  cov- 
ered with  a  colored  chart.  On  the  central  disk 
is  the  general  plan  of  the  Solar  System,  in- 


—17— 

eluding  all  the  Planets,  their  satellites,  and  a 
comet,  with  their  corresponding  sizes  and  dis- 
tances, as  near  as  practicable.  The  perihelion 
point  of  each  Planet  is  marked  in  its  orbit  with 
the  letter  P.  The  Planets  all  move  in  the  same 
general  direction  around  the  Sun  as  that  of  the 
Earth.  On  the  main  portion  of  the  stand,  and 
extending  to  the  edge,  the  chart  shows  the 
months  of  the  year,  and  their  divisions  into 
days ;  the  different  signs  of  the  zodiac  through 
which  the  Sun  will  pass  any  month  or  day ;  the 
right  ascension  of  the  Sun  in  hours  and  de- 
grees for  any  day;  the  number  of  minutes  the 
Sun  is  slow  or  fast  for  any  day  in  the  year; 
the  autumnal  and  vernal  equinoxes;  the  sum- 
mer and  winter  solstices;  the  aphelion  and 
perihelion;  when  the  seasons  begin,  etc.  The 
chart  on  the  rim  shows  the  ecliptic  or  orbit  of 
the  Earth  through  the  great  zodiacal  bell, 
showing  the  signs  in  which  the  Earth  will  ap- 
pear, looking  from  the  Sun,  and  its  right  ascen- 
sion in  hours  and  degrees  for  any  day  in  the 
year;  the  astronomical  and  almanac  signs 
representing  each  particular  sign  of  the  zodiac. 
At  the  perihelion  point  the  Earth  is  shown  to 
be  several  inches  nearer  the  Sun  than  at  the 
aphelion. 

The  instrument  is  so  perfect  and  durable  in 
its  construction  that  nothing  less  than  actual 
violence  can  break  of  put  it  out  of  order,  and, 


—18— 

with  the  accompanying  instructions,  any  one 
can  operate  it,  and  understand  the  subjects 
designed  to  be  illustrated. 

The  object  of  this  highly  instructive  ap- 
paratus is  to  illustrate  and  simplify,  to  the  eye 
of  the  learner,  the  whole  theory  of  Celestial 
Mechanics,  including  the  rudiments  of  Astron- 
omy and  Mathematical  and  Astronomical  Geo- 
graphy. 

No  other  instrument  can  claim  but  a  small 
part  of  what  this  instrument  actually  does,  as 
the  Matlick  New  Tellurian  is  the  only  instru- 
ment that  correctly  represents  the  true  motions 
of  the  Earth  and  Moon,  showing  their  exact 
relation  to  each  other  and  to  the  Sun  for  each 
day  in  the  year.  There  are  no  fewer  than  one 
hundred  theorems  and  problems  included  with- 
in the  above  subjects  that  this  instrument  is 
capable  of  illustrating. 


SUN  BALL 

No.- 2 


SET  SCREW 
No.  8 


Shipped  Complete 
Assembled 


EARTH  ARM  SOCKET 
No.  7 


AXIS  ROD 

MOON  ARM   CONNECTION         No.  14 
No.  9 


MOON  ARM 
No.  4 

I    MOON  ARM 
CAM       j 
\       No.  10 

\ 

EARTH  ARM  CONNECTION 
No   6 


RELEASE  NUT 
No.  12 


MOON  ARM  STANDARD 
No.  11 


The  Earth 


The  form  of  the  Earth  is  very  nearly  that  of 
a  globe,  slightly  flattened  at  the  poles.  This 
figure  is  known  to  mathematicians  as  oblate 
spheroid.  This  flattening  at  the  poles  is  very 
slight,  being  about  l-300th  part  of  the  diameter 
of  the  Earth.  The  axial'  diameter  is  about 
twenty-six  miles  less  than  the  equatorial.  The 
circumference  of  a  great  circle  of  the  earth  is 
about  25,000  miles,  and  the  diameter  of  that 
circle  is  about  8,000  miles.  The  surface  of  the 
Earth  embraces  an  area  of  200,000,000  square 
miles,  of  which  50,000,000  is  land  and  the  re- 
mainder water.  For  the  convenience  of  de- 
termining positions  on  the  Earth,  certain 
imaginary  lines,  or  circles,  are  supposed  to  be 
drawn  upon  it. 

The  Axis  of  the  Earth  is  the  diameter  about 
which  it  revolves,  and  the  extremities  of  the 
axis  are  donominated  the  poles;  the  one  above 
the  equator  the  North  Pole,  and  the  one  below, 
the  South  Pole. 

The  Equator  is  a  great  circle,  at  equal  dis- 
tances from  the  poles,  and  dividing  the  Earth 
into  two  parts,  called  the  Northern  and  South- 
ern Hemispheres. 

The  Parallels  of  Latitude  are  small  circles 
parallel  to  the  Equator,  and  are  drawn  for 


—20— 

every  ten  degrees,  and  are  numbered,  from  the 
Equator  to  the  poles,  90°.,  North  !of  the  Equa- 
tor is  called  North  Latitude,  and  south  of  the 
Equator  is  called  South  Latitude.  The  width 
of  a  degree  of  latitude  is  69  1-6  miles. 

Meridians  are  great  circles  passing  from  the 
North  Pole  to  the  South  Pole,  and  crossing  the 
Equator  at  right  angles.  Upon  the  globe  used 
on  the  Tellurian  to  represent  the  Earth,  the 
meridians  are  marked  every  15°,  which  cor- 
responds to  one  hour  of  time.  That  is,  it  will 
require  one  hour  for  the  vertical  rays  of  the 
Sun  to  pass  over  15°  of  longitude.  These  cir- 
cles are  numbered  to  the  east  180°  and  to  the 
west  180°,  from  the  meridian  of  Greenwich, 
which  passes  near  London.  East  of  this  estab- 
listed  meridian  is  called  East  Longitude,  and 
west,  West  Longitude.  The  width  of  a  degree 
of  longitude  on  the  Equator  is  69  1-6  miles,  but 
terminates  at  the  poles,  where  the  width  is  0. 

The  Tropics.  It  will  be  observed,  in  the 
motion  of  the  Tellurian,  that  the  vertical  rays 
of  the  Sun  fall  upon  the  Earth  23y2°  north  and 
23y2°  south  of  the  Equator,  when  the  Earth  is 
in  different  points  of  its  'orbit,  marking, 
respectively,  the  Tropic  of  Cancer  and  the 
Tropic  of  Capricorn.  The  day  circle  of  the 
Earth,  at  the  point  where  the  vertical  rays  are 
farthest  north,  will  show  that  the  rays  of  the 
Sun  shine  23i/20  beyond  the  North  Pole,  and 


21 

fall  23y2°  short  of  reaching  the  South  Pole,  or 
when  the  vertical  rays  are  farthest  south  the 
reverse  of  this  order  will  be  the  result.  These 
positions  of  the  Sun's  rays  to  the  Earth  mark 
the  Arctic  Circle,  23y2°  from  the  North  Pole, 
and  the  Antarctic  Circle,  231/2°  from  the  South 
Pole. 

Zones.  We  thus  see  why  the  Earth  is 
naturally  divided  into  five  zones.  The  region 
north  and  south  of  the  Equator,  and  between 
the  Tropics  of  Cancer  and  Capricorn,  over 
which  pass  the  vertical  rays  of  the  Sun,  is 
called  the  Torrid  Zone,  and  is  47°  in  width. 
The  region  between  the  Tropic  of  Cancer  and 
the  Arctic  Circle  is  called  the  North  Temperate 
Zone,  43°  in  width.  The  region  between  the 
Tropic  of  Capricorn  and  the  Antarctic  Circle, 
the  South  Temperate  Zone,  43°  in  width.  The 
regions  beyond  the  polar  circles  are  called  the 
North  and  South  Frigid  Zones. 

Daily  Motion.  If  we  observe  the  positions 
of  the  Sun,  Moon  and  Stars  for  a  few  succes- 
sive nights,  we  shall  see  their  relative  positions 
gradually  change.  In  our  observations  for  any 
day  or  night,  all  the  heavenly  bodies  appear  to 
move  to  the  west.  The  motions  are,  of  course, 
only  apparent,  as  there  is  absolute  proof  of 
the  motions  of  the  Earth  in  an  opposite  direc- 
tion to  the  apparent  motion  of  the  heavenly 
bodies.  All  the  apparent  motion  of  the  heaven- 


—22— 

ly  bodies  that  seemingly  pass  to  the  westward, 
is  the  result  of  the  daily  revolution  of  the 
Earth  on  its  axis  to  the  east.  As  a  result  01 
the  diurnal  motion  of  the  Earth,  we  see  the 
Sun  rise  in  the  east  and  set  in  the  west  each 
day,  producing  day  and  night.  When  the  Sun 
passes  below  the  horizon  its  light  is  no  longer 
visible,  and  one-half  the  Earth  is  wrapped  in 
darkness.  As  the  pin  in  the  center  of  the  solar 
semi-circle  band  indicates  noon  (on  any  merid- 
ian brought  to  it,  so  the  meridian  on  the  oppo- 
site side  of  the  Earth  must  indicate  mid-night ; 
consequently  to  an  observer  on  the  midnight 
meridian,  the  Earth  is  directly  between  him  and 
the  Sun.  Strictly  speaking,  the  Earth  revolves 
on  its  axis  in  about  23  hours  and  56  minutes, 
but,  as  the  Earth  is  continually  changing  its 
longitude,  the  day  is  24  hours  long.  It  will, 
therefore,  make  366  revolutions  in  a  year  of 
365  days. 

Difference  in  the  Length  of  Day  and  Night. 

Since  the  Sun  shines  on  but  one-half  of  the 
Earth  at  a  time,  it  is  evident  that  at  the 
Equator  the  days  and  nights  must  always  be  of 
equal  length.  If  the  axis  of  the  Earth  were 
perpendicular  to  the  plane  of  the  ecliptic,  so 
that  the  Sun  always  shone  from  pole  to  pole, 
the  days  and  nights  would  forever  be  of  the 
same  length  on  all  parts  of  the  Earth.  But  to 
an  observer,  on  any  parallel  north  or  south  of 


—23— 

the  Equator,  the  length  of  the  days  and  nights 
will  vary  in  different  parts  of  the  year,  and  the 
nearer  he  approaches  the  poles  the  greater  will 
be  the  difference,  until  he  reaches  the  poles, 
where  the  days  and  nights  are  alternately  six 
months  in  length.  Sometimes  the  days  are 
longest,  and  again  the  nights.  These  differ- 
ences are  regular  and  uniform,  and  their  re- 
currence is  the  same  for  each  year. 

Annual  Motion.  The  various  changes  in  the 
length  of  day  and  night  must  be  looked  for 
from  another  cause  than  the  rotation  of  the 
Earth  on  its  axis.  In  observing  the  fixed  Stars, 
it  will  be  noticed  that  they  do  not  appear  on 
the  same  meridian  at  the  same  time  each  night, 
but  about  four  minutes  earlier,  so  that  they 
appear  to  have  a  general  motion  to  the  west,  in 
addition  to  their  apparent  diurnal  motion. 
Any  particular  Star  seen  to  rise  in  the  east  at 
a  certain  hour  in  the  night  will  be  seen  to 
gradually  course  its  way  across  the  heavens  so 
that  in  six  months  from  that  night,  at  a  cor- 
responding hour,  it  will  fall  below  the  western 
horizon.  It  will,  of  course,  rise  and  set  each 
day  or  night,  but  will  come  to  the  meridian 
earlier  each  night.  From  this  and  other  causes 
it  has  been  fully  demonstrated  that  the  Earth 
has  an  annual  course  around  the  Sun  from  the 
west  to  east.  By  this  motion  the  Sun  appears 
to  be  carried  around  the  ecliptic  through  the 


—24— 

fixed  Stars.  Now,  as  the  Sun  appears  high  in 
the  heavens  in  one  part  of  the  ecliptic,  and 
again  falls  toward  the  horizon,  it  is  evident 
that  the  Earth's  axis  is  not  perpendicular  to 
the  plane  of  the  ecliptic,  but  inclines  from  this 
perpendicular.  It  is  found  that  the  Sun's  high- 
est and  lowest  meridian  altitude  differ  47°. 
Now,  one-half  of  this,  or  23%°,  must  represent 
the  inclination  of  the  Earth's  axis,  and  the 
Earth's  Equator  must  necessarily  make  an 
angle  with  the  plane  of  the  ecliptic  of  23%°. 

The  Poles.  The  North  Pole  of  the  Earth 
is  denominated  the  elevated  pole,  because  it  is 
always  about  66%  °  above  the  plane  of  the 
ecliptic,  or  about  23%°  from  a  perpendicular  to 
the  plane  of  the  ecliptic;  and  the  South  Pole  is 
denominated  the  depressed  pole,  because  it  is 
about  66%°  below  the  plane  of  the  ecliptic,  and 
23%°  from  a  perpendicular  to  the  plane.  These 
motions  and  the  direction  of  the  Earth's  axis 
are  so  perfectly  represented  in  the  Tellurian 
that  the  student  cannot  fail  to  comprehend  the 
entire  subject. 

The  Day  Circle  on  the  globe,  as  used  on  the 
Tellurian,  when  properly  adjusted,  shows 
exactly  the  portion  of  the  Earth  illuminated 
each  day,  and  the  variation  in  the  lengths  of 
day.  So  the  learner's  attention  is  directed 
wholly  to  it  at  the  present.  At  the  Vernal 
Equinox  the  Sun's  rays  shine  from  pole  to 


—25— 

pole,  but,  as  the  Earth  moves  along  in  its  orbit, 
the  North  Pole  is  gradually  turned  into  the 
sunlight,  and  the  South  Pole  into  the  darkness, 
until  the  Earth  arrives  at  the  summer  solstice 
—June  21 — when  the  North  Frigid  Zone  is 
\vliolly  in  the  sunlight,  and  the  South  in  dark- 
ness. It  will  be  seen  that  for  six  months  tne 
days  in  the  Northern  Hemisphere  hctve  grad- 
ually increased  in  length,  and  in  the  Southern 
Hemisphere  have  diminished.  They  are  now 
longest  north  of  the  Equator  and  shortest 
south.  Now,  as  the  Earth  is  moved  around  to 
the  autumnal  equinox,  the  days  naturally  di- 
minish in  length  in  the  Northern  Hemisphere, 
and  increase  in  the  Southern  Hemisphere,  until 
they  are  again  equal.  If  the  motion  is  con- 
tinued to  the  winter  solstice — December  21— 
the  days  in  the  Northern  Hemisphere  will  be 
shortest,  arid  in  the  Southern  Hemisphere  long- 
est. The  North  Frigid  Zone  is  wholly  in  dark- 
ness, and  the  South  Frigid  Zone  in  the  sun- 
light. For  any  day  between  these  dates  the 
day  circle  will  show  the  corresponding  lengths 
of  day  and  night  on  any  portion  of  the  Earth. 
The  length  of  a  parallel  on  the  Earth  shown 
by  the  day  circle  to  be  illuminated,  as  com- 
pared by  that  portion  on  the  opposite  side,  will 
indicate  their  relative  lengths.  The  meridians 
marked  on  the  Earth,  followed  to  the  hori- 
zontal band  with  the  24  hours  of  day  and  night 


—26— 

on  the  dark  and  illuminated  sides,  will  serve  as 
a  means  of  measurement. 

When  the  Sun  Rises,  and  When  It  is  Mid- 
night at  the  Poles.  When  the  Sun  passes  the 
vernal  equinox,  it  rises  to  the  Arctic,  'or  elevat- 
ed, Pole,  and  sets  to  the  Antarctic  Pole.  When 
the  Sun  arrives  at  the  summer  solstice  it  is 
noon  at  the  North  Pole,  and  midnight  at  the 
South  Pole.  When  the  Sun  passes  the 
autumnal  equinox,  it  sets  to  the  North  Pole, 
and  rises  to  the  South  Pole.  When  the  Sun 
arrives  at  the  Winter  solstice,  it  is  midnight  at 
the  North  Pole,  and  noon  at  the  South  Pole; 
and  when  the  Sun  comes  again  to  the  vernal 
equinox,  it  closes  the  day  at  the  South  Pole, 
and  lights  up  the  morning  at  the  North  Pole. 


—Illustrating  Kepler* s  Second  Law. 
Fig.  1. 

The  illuminating  band,  or  day  circle,  on  the 
Earth,  will  show  how  the  sunlight  approaches 
or  recedes  from  the  pole. 

The  Nights  at  the  Poles  Not  Equal.  By  con- 
sulting an  almanac  for  any  year  one  discovers 
that  the  time  required  for  the  Sun  to  make  its 
apparent  journey  from  the  autumnal  equinox 


—27— 

to  the  vernal  equinox  is  V7Sy2  days,  while  from 
the  vernal  equinox  to  the  autumnal  requires 
186V2  days.  This  results  from  what  is  known 
as  Kepler's  second  law  of  planetary  motion. 
(Fig.  1).  The  radius  vector  describes  equal 
areas  in  equal  times.  That  is,  in  our  winter, 
the  Earth  being  in  perihelion,  moves  more  rap- 
idly in  its  orbit  than  when  in  aphelion.  This 
is  clearly  exhibited  by  the  Telurian. 

Night  Within  the  Polar  Circle.  At  the  Arc- 
tic Circle,  23°  27y2'  from  the  Pole,  the  longest 
day  is  24  hours,  and  goes  on  increasing  as  you 
approach  the  Pole.  In  latitude  67°  18'  it  is  30 
days;  in  latitude  69°  30'  it  is  60  days,  etc.  The 
same  takes  place  between  the  Antarctic  Circle 
and  the  South  Pole,  with  the  exception  that  the 
day  in  the  same  latitude  south  is  a  little 
shorter,  since  the  Sun  is  not  S'o  long  south  of 
the  Equator  as  north  of  it.  At  Spitzbergen  the 
day  gradually  increases  in  length  from  the  first 
glimpse  of  the  Sun  on  February  21,  to  12  hours 
on  March  21;  then  to  24  hours  on  April  21, 
when  the  Sun  remains  continuous  above  the 
horizon  until  August  21.  The  day  then  alter- 
nates with  night,  decreasing  from  24  hours  to  a 
parting  glimpse  on  October  21,  when  night  con- 
tinues for  four  months.  In  the  southern  part 
of  Nova  Zembla  we  find  continuous  day  and 
night  of  about  six  weeks  each,  and  then  day 
and  night  alternate  for  twenty  weeks  each. 


—28— 

Further  north,  the  periods  of  alternate  day  and 
night  are  shorter,  decreasing  to  the  Pole.    At 
Wanderbus,  in  Norway,  the  day  lasts  from  the 
21st  of  May  to  the  22d  of  July,  without  inter 
ruption. 

Day   in   the   Temperate   and   Torrid   Zones. 

The  greatest  length  of  day  in  the  Torrid  Zone, 
which  must  be  on  the  tropics,  is  13Vi>  hours. 
The  greatest  length  of  day  in  the  Temperate 
Zone,  which  must  be  on  the  polar  circle,  is  24 
hours.  At  Portland,  Oregon,  the  longest  day 
has  151/2  hours;  at  Boston,  IS1/!;  at  Berlin  and 
London,  IG1/^;  at  Stockholm  and  Upsaal,  IB1/-!*; 
at  Hamburg,  Dantzic  and  Stettin,  17,  and  the 
shortest,  7.  At  St.  Petersburg  and  Tobolsk  the 
longest  day  has  19,  and  the  shortest  5  hours. 
At  Bornea,  in  Finland,  the  longest  day  has 
21%,  and  the  shortest  2y2  hours.  The  night 
must,  in  all  cases,  be  24  hours,  minus  the  length 
of  the  day,  and  vice  versa.  As  the  change  of 
the  Sun's  declination  is  less  at  the  solstices 
than  at  the  equinoxes,  so  the  change  in  the 
relative  length  of  day  and  night  must  also  ho 
variable  in  the  same  places.  To  illustrate  this 
point  more  fully,  the  learner's  attention  is 
called  to  the  position  of  the  Earth  to  its  orbit. 
It  will  be  noticed  that  at  the  equinoxes  the 
Earth  moves  in  a  direction  very  nearly  indi- 
cated by  its  axis;  so  that  from  March  21  to 
April  21  the  Sun  moves  northward  about  10°, 


—29— 

and  from  April  21  to  May  21  about  9°,  and 
from  May  21  to  June  21  about  4° ;  so  that  the 
Sun  changes  its  declination  very  slowly  at  the 
solstices,  as  the  Earth  then  is  moving  very 
nearly  in  a  direction  indicated  by  a  parallel  of 
the  Earth.  The  same  cause  somewhat  affects 
the  apparent  diurnal  motion  'of  the  Sun  to  and 
from  the  noon  point. 

It  follows  that  during  the  year  every  portion 
of  the  Earth  must  have  an  equal  amount  of  day 
and  night;  that  is,  there  must  be  in  all  parts 
six  months  day  and  six  months  night.  In  these 
estimates  no  account  is  taken  of  the  refraction 
of  the  atmosphere,  which  increases  the  length 
of  the  day,  by  making  the  Sun  appear  more 
elevated  above  the  horizon  than  it  really  is. 

To  Determine  When  the  Sun  Rises  and  Sets, 

By  observing  the  circle,  the  time  the  Sun  will 
rise  or  set  can  be  determined,  as  well  as  the 
length  of  day  or  night.  To  determine  when  the 
Sun  will  rise  or  set  at  any  particular  point, 
mark  where  the  parallel  of  the  given  point  in- 
tersects the  day  band,  and  trace  the  meridian 
directly  to  where  it  intersects  the  horizontal 
band  marked  with  the  hour  of  the  day  or  night. 
This  point  of  intersection  will  show  the  exact 
time  of  the  rising  and  setting  of  the  Sun. 


—30— 

From  this  the  length  of  day  and  night  can  be 
determined  easily  for  any  day  in  the  year. 

To  find  when  the  Sun  rises  and  sets  in  any 
region  where  the  day  or  night  is  more  than  24 
hours  long,  move  the  arm  around  and  notice 
the  date  that  that  portion  of  the  Earth  appears 
on  the  illuminated  side  of  the  day  circle,  which 
will  give  the  date  'of  the  Sun 's  appearance,  arid 
the  portion  that  passes  on  the  dark  side,  for 
the  disappearance  of  the  Sun. 

The   Earth's   Orbit   and   the  Zodiacal  Belt. 

The  Earth's  orbit  around  the  Sun  is  elliptical, 
as  shown  by  the  top  of  the  stand  of  the  Tellu- 
rian. This  is  exaggerated,  or  is  more  elongat- 
ed than  if  drawn  to  a  true  scale,  but  it  serves 
to  bring  more  forcibly  to  the  eye  the  ellipticity 
of  the  Earth's  orbit.  The  Sun  occupies  one  of 
the  foci  of  the  ellipse,  so  that  the  Earth,  in  its 
course  around  the  Sun,  is  brought  very  much 
nearer  to  the  Sun  in  one  point  of  its  orbit  than 
in  another.  The  Earth  is  in  perihelion  Jan- 
uary 1,  when  it  is  91,000,000  miles  from  the 
Sun,  and  in  aphelion  July  1,  when  it  is  about 
94,000,000  miles  distant,  being  about  3,000,000 
miles  nearer  the  Sun  in  one  part  of  its  'orbit 
than  another.  These  points  are  plainly  shown 
by  the  Tellurian. 

The  great  belt  of  the  heavens  through  which 
the  Earth  and  Sun  appear  to  travel  is  called 
the  zodiac.  This  belt  extends  about  8°  on  each 


—31— 

side  of  the  ecliptic,  and  is  shown  by  the  chart 
on  the  rimi  of  the  stand.  The  orbits  of  all  the 
major  Planets  in  the  solar  system  lie  within 
this  belt.  The  Sun  appears  to  travel  through 
this  belt  as  the  Earth  makes  its  annual  journey 
around  the  ecliptic.  Commencing  with  the 
position  of  the  Sun  at  the  vernal  equinox,  the 
early  astronomer  divided  the  ecliptic  into 
twelve  signs,  of  30°  each,  and  afterwards  gave 
the  following  names  to  them:  Aries,  Taurus, 
Gemini,  Cancer,  Leo,  Virgo,  Libra,  Scorpio, 
Sagittarius,  Capricornus,  Aquarius  and  Pisces. 
At  first,  or  about  2,200  years  ago,  the  constella- 
tions of  Stars  corresponded  with  the  sign  in 
name,  but,  owing  to  the  precession  of  the 
equinoxes,  which  will  be  explained  hereafter, 
the  constellations  and  signs  have  entirely 
changed,  so  that  the  constellation  Pisces  occu- 
pies the  sign  Aries,  and  the  constellation  Aries 
the  sign  Taurus. 

When  the  Sun  appears  to  us  to  be  in  one 
part  of  the  ecliptic,  the  Earth,  as  seen  from  the 
Sun,  appears  in  the  point  diametrically  op- 
posite. Thus,  when  the  Sun  appears  in  the 
vernal  equinox  at  the  first  point  of  Aries,  the 
Earth  is  actually  in  the  opposite  equinox  at 
Libra.  This  may  be  observed  by  looking  on  the 
top  plate  on  the  top  of  the  stand  for  the  sign 
in  which  the  Sun  appears,  and  on  the  rim  for 


—32— 

the  sign  in  which  the  Earth  will  be  at  a  given 
time. 

We  have  no  historic  record  of  this  division 
of  the  zodiac  into  signs,  and  the  ideas  of  the 
authors  can  only  be  inferred  from  collateral 
circumstances.  It  has  been  fancied  that  the 
names  were  suggested  by  the  seasons,  the  agri- 
cultural operations,  and  so  on.  Thus,  the 
spring  signs — Aries  the  Earn,  Taurus  the  Bull, 
and  Gemini  the  Twins — are  supposed  to  mark 
the  bringing  forth  of  young  by  the  flocks  and 
herds.  Cancer,  the  Crab,  marks  the  time  when 
the  Sun,  having  attained  its  greatest  declina- 
tion begins  to  go  back  toward  the  Equator;  and 
the  Crab  having  been  supposed  to  move  back- 
wards, his  name  was  given  to  this  sign.  Leo, 
the  Lion,  symbolizes  the  fierce  heat  of  summer. 
Virgo,  the  Virgin,  gleaning  corn,  symbolizes 
the  harvest.  In  Libra,  the  Balances,  the  day 
and  night  balance  each  other,  being  of  equal 
length.  Scorpio,  the  Scorpion,  is  supposed  to 
have  marked  the  presence  of  venomous  reptiles 
in  October,  while  Sagittarius,  the  Archer,  sym- 
bolizes the  season  of  hunting.  The  explanation 
of  Capricornus,  the  Goat,  is  more  fanciful,  if 
possible,  than  that  of  Cancer.  It  was  supposed 


—33— 

that  the  animal,  ascending  the  hill  as  he  feeds, 
in  order  to  reach  the  grass  more  easily,  on 
reaching  the  top,  turns  back  again,  so  that  his 
name  was  used  to  mark  the  sign  in  which  the 
Sun,  from  going  south,  begins  to  return  to  the 
north.  Aquarius,  the  Water  Bearer,  symbol- 
izes the  winter  rains,  and  Pisces,  the  Fishes, 
the  season  of  fishes. 


Change  of  Seasons 


Effects    of  Heat   and   Cold — Their  Causes. 

All  the  perceptible  changes  of  the  seasons  are 
brought  about  by  the  difference  in  the  temper- 
ature of  the  atmosphere.  The  green  grass  of 
spring,  the  golden  grain  of  summer,  the  seared 
leaves  of  autumn,  and  the  drifting  snows  of 
winter,  are  the  results  of  heat  and  cold.  The 
next  question  which  arises  in  the  mind  of  the 
learner  is,  what  causes  these  various  temper- 
atures at  the  different  times  of  the  year,  and 
on  different  portions  of  the  globe!  As  the  in- 
ternal fires  of  the  Earth  have  little  or  no  effect 
at  its  surface,  it  is  evident  that  our  only  source 
of  heat  is  the  Sun.  The  intensity  of  heat  de- 
pends mainly  upon  the  direction  with  which  the 
Sun's  rays  fall  upon  the  Earth.  It  has  been 
demonstrated  that  as  much  heat  is  produced 
upon  the  same  area  from  a  vertical  Sun  in 
eight  hours  as  would  be  produced  at  an  agle  of 
60°  in  sixteen  hours.  Whether  the  rays  fall 
on  a  particular  point  of  the  Earth  vertically 
or  obliquely  depends  upon  the  relative  position 
of  the  Earth  to  the  Sun.  An  additional  cause 
of  the  different  temperature  is  found  in  the 
fact  that  when  the  Sun  is  above  the  horizon 


—35— 

at  any  place,  at  that  place  the  Earth  is  re- 
ceiving heat;  and  when  the  Sun  is  below  the 
horizon,  it  is  parting  with  its  heat,  by  a  pro- 
cess which  is  called  radiation.  The  quan- 
tities of  heat  thus  received  and  imparted  in 
the  course  of  the  year  must  balance  each 
other  at  every  place,  or  the  equilibrium  of  tem- 
perature would  not  be  supported.  Whenever 
the  Sun  remains  more  than  twelve  hours  above 
the  horizon  of  any  place,  the  general  temper- 
ature of  that  place  will  be  above  the  mean 
state;  when  the  reverse  takes  place,  the  tem- 
perature, for  the  same  reason,  will  be  below 
the  mean  state.  The  continuance  of  the  Sun 
above  the  horizon  of  any  place  depends  entirely 
upon  his  declination  or  altitude  at  noon,  and 
this  also  determines  the  angle  at  which  the 
rays  fall  upon  the  Earth  at  that  point.  Thus, 
the  two  causes  of  heat  necessarily  act  at  the 
same  time,  for  the  rays  of  the  Sun  are  always 
most  vertical  when  it  shines  longest  above  the 
horizon.  The  axis  of  the  Earth  is  inclined  to 
the  plane  of  its  orbit,  and  thus  it  is  that  in  the 
course  of  its  annual  revolution  around  the  Sun 
the  rays  fall  at  different  angles  on  every  por- 
tion of  the  globe. 

The  manner  in  which  the  Earth  changes  its 
relative  position  to  the  Sun  during  its  yearly 
revolution  is  perfectly  represented  by  the  Tel- 
lurian. 


Winter 


Place  the  Earth  and  Moon  in  position,  as 
previously  explained  and  shown  in  Fig.  2.  At 
this  point,  December  21,  the  Northern  Hem- 
isphere will  have  its  greatest  inclination  from 
the  Sun,  and  the  rays  of  the  Sun  will  fall  more 
obliquely  upon  this  portion  of  the  Earth,  and 
will  be  less  effective  in  producing  heat,  and  in 
the  Southern  Hemisphere  the  rays  will  fall 
more  nearly  vertical,  consequently  more  heat 
will  be  the  result.  Thus,  while  the  Northern 
Hemisphere  has  winter,  the  Southern  Hem- 
isphere will  have  summer.  The  Earth  is  now 
at  the  winter  solstice. 

The  Arctic  Circles  and  Tropic  of  Capricorn. 

At  this  point  the  rays  of  the  Sun  will  not  reach 
the  North  Pole  by  23y2°,  and  will  shine  23y2° 
beyond  or  under  the  South  Pole  marking  the 
Arctic  and  the  Antarctic  Circles.  The  vertical 
rays  of  the  Sun  will  fall  23y2°  south  of  the 
Equator,  and  mark  the  Tropic  of  Capricorn; 
this  marks  the  beginning  of  winter  in  the 
Northern  Hemisphere,  and  the  beginning  of 
summer  in  the  Southern  Hemisphere.  The 
Earth  now  enters  the  sign  of  Cancer,  and  the 
Sun  the  sign  of  Capricorn.  It  will  now  be  con- 


Figs.    2    and    6. 


48 


Fig.  3. 


—37— 

tinual  night  at  the  North  Pole  and  continual 
day  at  the  South  Pole.  At  this  time  the  Sun 
does  not  shine  half  way  around  the  Earth  in 
the  Northern  Hemisphere,  and  on  more  than 
half  the  Southern  Hemisphere ;  that  is,  the  Sun 
will  shine  on  less  than  180°  of  a  given  parallel 
in  the  Northern  Hemisphere,  and  on  more  than 
180°  of  a  given  parallel  in  the  Southern  Hem- 
isphere. A  few  days  later,  or  the  1st  of  Jan- 
uary, the  Earth  is  in  perihelion,  or  nearest  to 
the  sun. 


Spring 


Pass  the  Earth  around  so  that  the  long  rod 
is  directly  over  March  20,  the  vernal  equinox. 
At  this  point  the  Earth  neither  inclines  to  nor 
from  the  Sun,  and  the  days  and  nights  are 
eqnal  in  all  parts  of  the  Earth,  as  the  Sun 
shines  from  Pole  to  Pole,  and  the  vertical  rays 
fall  directly  upon  the  Equator.  This  marks  the 
beginning  of  spring  in  the  Northern  Hem- 
isphere, and  the  beginning  of  autumn  in  the 
Southern  Hemisphere.  The  vertical  rays  are 
traveling  northward,  bringing  warmth  and  heat 
into  the  Northern  Hemisphere,  and  gradually 
receding  from  and  leaving  it  cold  and  bleak  in 
the  Southern  Hemisphere.  At  this  point  the 
Earth  enters  the  sign  of  Libra,  and  the  Sun  the 
sign  of  Aries. 


Summer 


Continue  the  movement  of  the  Earth  around 
to  June  21,  the  summer  solstice,  at  which  point 
the  Northern  Hemisphere  of  the  Earth  will 
lean  toward  the  Sun,  and  the  rays  will  strike 
more  directly  upon  the  portion  of  the  Earth 
north  of  the  Equator,  and  obliquely  upon  the 
Southern  Hemisphere.  This  marks  the  begin- 
ning of  summer  in  the  Northern  Hemisphere, 
and  the  beginning  of  winter  in  the  Southern 
Hemisphere.  The  rays  of  the  Sun  now  fall 
vertically  upon  the  Earth  23%°  north  of  the 
Equator,  and  mark  the  Tropic  of  Cancer,  and 
also  shine  23i//  beyond  the  North  Pole.  (Fig. 
3.) 

The  Tronic  of  Cancer  and  the  Arctic  Circle. 

At  the  Tropic  of  Cancer  the  vertical  rays  have 
reached  their  farthest  point  north  of  the  Equa- 
tor, and  from  there  start  south  again.  At  this 
point  continual  day  exists  in  the  North  Frigid 
Zone,  and  continual  night  in  the  South  Frigid 
Zone.  The  Earth  at  this  time  enters  the  sign 
of  Capricorn  and  the  Sun  the  sign  of  Cancer. 
A  few  days  later,  or  July  1,  the  Earth  is  in 
aphelion,  or  farthest  from  the  Sun. 


Autumn 


Move  the  Earth  around  to  September  22,  the 
autumnal  equinox,  which  marks  the  beginning 
of  autumn  in  the  Northern  Hemisphere,  and 
spring  in  the  Southern  Hemisphere,  at  which 
point  the  Earth  again  neither  inclines  to  nor 
from  the  Sun,  and  the  days  and  nights  are 
equal  throughout  the  Earth.  The  Earth  now 
enters  the  sign  of  Aries,  and  the  Sun  Libra. 
By  continuing  the  movement  of  the  Earth  until 
it  again  arrives  at  December  21,  it  will  have 
completed  its  yearly  revolution,  showing  the 
proper  positions  of  the  Earth  and  Moon  in 
relation  to  the  Sun  every  day  during  the  year ; 
remembering  that  the  Earth  should  revolve  on 
its  axis  every  day,  and  that  the  North  Pole  of 
the  Earth  should  at  all  time  point  in  the  same 
direction. 

The  True  Cause  of  Temperature.  Now,  as 
the  Sun's  rays  fall  most  obliquely  when  the 
days  are  shortest,  and  most  directly  when  the 
days  are  longest,  these  two  causes,  namely,  the 
duration  and  intensity  of  the  solor  heat,  to- 
gether, produce  the  temperature  of  the  differ- 
ent seasons.  The  reason  why  we  have  not  the 
hottest  temperature  when  the  days  are  longest, 


—41— 

and  the  coldest  temperature  when  the  days  are 
shortest,  but  in  each  case  about  a  month  after- 
wards, appears  to  be  that  a  body  once  heated 
does  not  grow  cold  instantaneously,  but  grad- 
ually; and  so  of  the  contrary.  Hence,  as  long 
as  more  heat  comes  from  the  Sun  by  day  than 
is  lost  by  night,  the  heat  will  increase,  and  vice 
versa. 

Our  Winter  When  Nearest  the  Sun.  It  may 
seem  strange  to  the  learner  that  we  have  our 
winter  when  nearest  the  Sun,  and  our  Summer 
when  most  distant;  but  it  must  be  remembered 
that  the  temperature  of  any  particular  part  of 
the  Earth  is  not  so  much  affected  by  the  dis- 
tance of  the  Sun  as  by  the  directness  or  ob- 
liqity  of  its  rays.  Hence,  though  we  are 
farther  from  the  Sun  on  the  21st  of  June  than 
on  the  21st  of  December,  yet  as  the  North  Pole 
of  the  Earth  is  turned  more  directly  into  the 
light  at  that  time,  so  that  the  Sun's  rays  strike 
its  surface  less  obliquely  than  in  December,  we 
have  a  higher  temperature  at  that  period, 
though  at  a  greater  distance  from  the  Sun. 


Twilight 


When  the  Sun  is  below  the  horizon,  the  rays 
passing  through  the  upper  portion  of  the 
atmosphere  are  reflected  and  refracted  by  the 
molecules  of  the  air,  so  that  we  are  enabled  to 
see  objects  by  this  reflected  light,  called  twi- 
light, at  the  dawn  and  close  of  day,  some  time 
before  the  appearance,  and  after  the  disappear- 
ance, of  the  direct  rays  of  the  Sun.  The  length 
or  duration  of  twilight  depends  on  many  con 
ditions.  The  atmosphere  extends  upward 
about  80  miles,  and  in  cold  regions  the  reflec- 
tion and  refraction  is  much  greater  than  in 
warmer  regions.  Generally  twilight  extends 
from  15°  to  18°  beyond  the  portion  illuminated 
by  the  direct  rays.  The  duration  at  the  Equa- 
tor is  about  one  hour,  or  a  few  minutes  more  at 
certain  times,  as  when  the  Sun  is  at  the  sol- 
stice. In  higher  latitudes,  or  further  north  or 
south,  the  duration  is  much  greater.  Stock- 
holm has  a  period  of  twilight  lasting  from 
sunset  to  sunrise  for  a  period  of  four  months. 
On  the  85th  parallel  twilight  lasts  for  twenty - 
eight  days.  These  periods  are,  of  course,  when 
the  Sun  has  its  greatest  declination  north.  The 
same  would  be  noticed  in  corresponding  lati- 


—43— 

tudes  south  when  the  Sun  has  its  declinations 
south.  The  day  circle  on  the  Earth,  as  used  in 
the  Tellurian,  will  fully  illustrate  these  sub- 
jects. As  twilight  extends  about  15°  to  18°  be- 
yond this  band,  its  duration  can  be  fully  de- 
termined by  observing  the  time  required  for 
any  particular  point  15°  to  18°  beyond  this 
circle  to  be  brought  into  the  direct  rays  in  the 
diurnal  and  annular  motions  of  the  Earth. 


The  Moon 


With  the  exception  of  the  Sun,  our  interest 
in  the  Moon  is  greater  than  in  that  of  any 
other  heavenly  body,  as  it  is  by  far  the  nearest 
to  us.  Its  mean  distance  from  the  Earth  is 
about  240,000  miles,  but,  owing  to  the  ellip- 
ticity  of  its  orbit  and  the  attractive  force  of  the 
Sun,  it  varies  from  10,000  to  20,000  miles  upon 
each  side  of  this  mean  during  each  monthly 
revolution,  with  an  average  oscillation  on  each 
side  of  13,000  miles.  The  greatest  possible 
distance  is  259,600  miles,  and  the  least  dis- 
tance is  221,000  miles  from  the  Earth;  but  it 
rarely  approaches  these  limits.  The  conditions 
required  to  produce  this  great  oscillation  are 
the  Earth  to  be  in  a  perihelion  and  the  Moon 
in  apogee,  and  in  conjunction,  for  the  greater 
distance;  and  the  Moon  in  perigree  and  in  op 
position,  for  the  least  distance.  The  Moon's 
diameter  is  2,160  miles,  or  a  little  less  than 
two-seventh  that  of  the  Earth;  its  volume  is, 
therefore,  about  one-fiftieth  that  of  the  Earth, 
but  owing  to  the  greater  density  of  the  Earth, 
its  mass  is  only  about  one-eightieth. 

The  Axial  Revolution  of  the  Moon.    One  of 
the  most  remarkable  features  of  the  Moon  is, 


44 


Plate  III. 
The  Moon. 


that  it  revolves  once  on  its  axis  while  making- 
one  complete  lunation,  consequently  presents 
the  same  face  to  the  Earth  continually,  so  that 
no  human  eye  has  ever  seen  but  one  side  of 
the  Moon.  The  lunar  day  is  29%  times  as  long 
as  the  terrestial  day.  The  Sun  will,  therefore, 
shine  on  the  Moon's  Equator  for  nearly  fifteen 
of  our  days,  and  will  not  be  seen  again  for 
the  same  period.  As  a  result  the  changes  of 
temperature  from  the  lunar  day  to  the  lunar 
night  are  very  great.  The  heat  of  the  day 
would  perhaps  be  far  greater  than  that  known 
anywhere  on  our  globe,  while  the  excessive 
cold  of  our  arctic  winter  would  hardly  equal 
that  of  the  lunar  night. 

On  the  Moon.  To  an  observer  on  one  side 
of  the  Moon  the  Earth  would  appear  like  an 
immense  Moon  passing  through  all  of  the 
phases,  but  would  never  set;  while  if  he  were 
on  the  other  side  of  the  Moon  this  terrestrial 
sphere  would  never  be  visible.  The  light  and 
dark  observed  upon  the  Moon  is  owing  to  the 
unequal  reflection  of  light  caused  by  the  great 
diversity  of  her  surface.  By  viewing  the  Moon 
through  a  telescope,  immense  mountains  and 
deep  crevices  and  craters  may  be  seen,  but  no 
water  ar  atmosphere  is  at  all  discernable;  and 
as  we  know  life,  it  could  not  exist  on  that  dead 
body.  By  the  most  careful  determination  yet 
made,  it  is  found  that  the  Sun  gives  619,000 


—46— 

times  as  much  light  as  a  full  Moon;  but,  while 
this  is  the  comparison  in  light  it  has  been  care- 
fully computed  that  the  Sun  only  gives  82,600 
times  as  much  heat.  This  discrepancy  is 
doubtless  owing  to  the  fact  that  the  Moon  has 
been  raised  to  such  a  high  temperature  by  the 
Sun's  rays  falling  upon  her  surface  continual- 
ly for  so  long  a  time,  that  the  Moon  would  thus 
reflect  much  of  her  heat. 

The  Effects  of  the  Attractive  Force  o<f  the 
Moon.  The  greatest  effect  of  the  Moon's  at- 
tractive force,  so  far  as  yet  understood,  has 
been  explained  in  the  phenomena  of  the  tides. 
There  is  also  a  tide  in  the  atmosphere,  pro- 
duced from  the  same  influence.  There  is  no 
evidence  that  the  Moon  affects  the  Earth,  or 
its  inhabitants,  in  any  other  way  than  by  its 
attraction.  It  is  not  improbable,  however, 
that,  owing  to  the  peculiar  relation  of  the  Sun 
and  Moon  at  times,  and  their  declination 
north  and  south,  producing  wonderful  changes 
in  atmospherical  tides,  that  storms  and  various 
changes  in  the  weather  would  be  the  result. 
A  thorough  investigation  of  these  causes  and 
effects  would  doubtless  do  much  to  establish 
the  true  law  of  storms. 

Phases  of  the  Moon.     To  explain  with  the 
Tellurian,  look  in  an  almanac  and  determine 
when  new  Moon  will  occur  the  nearest  to  Jan 
uary  1  and  bring  the  long  arm  over  that  date. 


Fig.    4. 


Pig.   5. 


—47— 

Throw  the  mechanism  "out  of  gear"  and 
bring  the  Moon  around  so  that  it  is  over  the 
long  arm  between  the  Earth  and  Sun.  This 
will  show  new  Moon.  Throw  in  gear.  In  1909 
new  Moon  occurred  on  January  21  and  if 
the  Tellurian  is  adjusted  for  that  date  and 
the  long  arm  moved  around  it  will  show  all 
the  phases  of  the  Moon  for  that  year,  and  for 
1910  it  will  show  new  Moon  on  January  11, 
thus  illustrating  accurately  the  phases  of  the 
Moon  for  any  year  or  number  of  years  and 
the  dates  of  their  occurrence.  Keep  the  light 
side  of  the  Moon  toward  the  Sun  in  explaining 
the  phases  of  the  Moon.  The  Moon,  being  an 
cpaque  body,  shines  by  the  reflected  light  of 
the  Sun.  At  this  point  the  light  of  the  Moon 
cannot  be  seen  from  the  Earth,  and  is,  there- 
fore, said  to  be  new  Moon,  or  in  conjunction. 
(Fig.  4.)  Move  the  rod  forward  a  short  dis- 
tance in  the  proper  direction,  and  a  small 
crescent  will  be  observed.  Continue  the  move- 
ment one-fourth  of  the  distance  in  its  orbit, 
and  one-half  the  light  side  will  be  seen,  which 
is  the  first  quarter  of  the  Moon  or  quadrature. 
(Fig.  5.)  Again,  move  the  bodies  forward  un- 
til the  Moon  is  directly  opposite  the  Earth 
from  the  Sun.  The  whole  face  of  the  Moon 
will  now  be  seen,  and  it  is  full  Moon  or  oppo- 
sition. (Fig.  6.)  Continue  the  movement  one- 
fourth  farther,  and  the  Moon  will  arrive  at 


third  quarter,  and  the  opposite  half  of  the  light 
side  of  the  Moon  will  be  seen  from  that  which 
was  shown  at  first  quarter.  It  is  again  in 
quadrature.  (Fig.  7.)  The  bodies  may  now 
be  moved  forward  until  the  Moon  is  again  in 
conjunction,  remembering  that  the  observer 
all  the  time  is  looking  from  the  Earth  beneath 
the  Moon. 

The  Movement  of  the  Moon.  The  time  re- 
quired for  the  Moon  to  move  from  new  Moon 
to  new  Moon  is  29%  days,  while  it  will  be  ob- 
served that  it  will  move  completely  around  the 
earth  in  27  1-3  days.  The  difference  in  these 
periods  is  occasioned  by  the  onward  move- 
ment of  the  Earth  in  its  orbit.  The  movement 
of  the  Moon  eastward  will  also  explain  the 
cause  of  the  Moon  rising  on  an  average  fifty 
minutes  later  each  day. 

Apogee  and  Perigee.  In  the  movement  of 
the  Moon  in  its  orbit,  it  will  be  observed  that 
the  Earth  and  Moon  approach  and  recede  from 
each  other.  The  nearest  approach  of  these 
bodies  is  called  perigee,  and  the  farthest  point 
apogee.  These  two  points  in  the  Moon's  orbit 
are  also  called  the  apsis,  and  the  line  connect- 
ing them  the  line  of  the  apsides. 

Declination  o<f  the  Moon.  The  declination 
of  the  Moon  north  or  south,  or  high  Moon  or 
low  Moon,  depends  on  two  things:  The  in- 


Fig.  7. 


Fig.  8. 


—49— 

clination  of  the  Moon's  orbit  to  the  plane  of 
the  ecliptic,  which  is  about  5°,  and  the  inclina- 
tion of  the  Earth  to  the  plane  of  the  ecliptic, 
but  mostly  the  latter,  which  will  be  observed 
by  the  Tellurian.  The  dim  face  of  the  whole 
disk  of  the  Moon,  when  only  a  part  of  the 
illuminated  side  is  seen,  is  due  to  the  reflec- 
tion of  the  light  from  the  Earth  on  the  Moon. 


Eclipses  of  the  Sun  and  Moon 


An  eclipes  of  the  Sun  and  Moon  has  always 
been  observed  with  great  interest,  and  their 
recurrence  terrified  the  ancients,  and  even  the 
superstitutious  of  modern  times.  A  close  ob- 
servation of  the  prenomena  soon  revealed  the 
fact  that  an  eclipse  of  the  Sun  always  took 
place  at  new  Moon,  and  of  the  Moon  at  full 
Moon,  so  that  the  motions  of  these  bodies  could 
not  be  watched  long  without  the  cause  being 
seen.  It  was  evident  that  if  the  Moon  should 
pass  between  the  Earth  and  Sun,  the  illumin- 
ating rays  would  be  obscured,  and  thus  we  find 
the  early  Astronomers  were  well  acquainted 
with  the  eclipses  and  their  cause. 

General  Cause  of  an  Eclipse.  If  the  Moon 
moved  on  the  same  plane  with  the  Earth,  it  is 
evident  that  an  eclipse  would  occur  at  every 
new  and  full  Moon,  but  as  the  orbit  of  the 
Moon  inclines  to  the  plane  of  the  ecliptic, 
about  5°,  the  Moon  will  generally  pass  above 
or  below  the  Sun,  and  consequently  there  will 
be  no  eclipse.  (Fig.  5.)  The  points  where  the 
Moon  crosses  the  ecliptic  are  called  the  Moon's 
nodes.  If  the  Moon  is  in  the  neighborhood  of 


—51— 

one  of  its  nodes  at  new  or  full  Moon,  there  will 
be  an  eclipse.     (Fig.  2.) 

Solar  Eclipses — Their  Nature  and  Causes, 
The  number  and  nature  of  eclipses  that  occur 
each  year  depend  upon  the  relation  of  the 
nodes  to  the  Sun  at  the  time  of  new  and  full 
Moon.  To  illustrate:  On  August  24,  1877,  the 
Sun  passed  the  Moon's  descending  node,  but 
the  times  of  new  Moons  nearest  to  that  date 
were  August  8  and  September  6.  At  the  first 
date  the  Moon  passed  above  or  north  of  the 
cliptic,  so  that  only  a  partial  eclipse  was  vis- 
ible in  the  northern  part  of  Siberia,  while  at 
the  latter  date  the  Moon  had  passed  so  far 
south  that  only  a  small  eclipse  was  visible  at 
Cape  Horn.  Thus,  there  were  two  solar 
eclipses  while  the  Sun  was  passing  the  one 
node,  but  very  small.  One  year  later,  1878, 
the  Sun  passed  the  node  about  August  4,  and 
the  new  Moon  occurred  on  July  29,  the  Moon 
being  so  close  to  the  node  that  a  total  eclipse 
was  visible.  Every  time  the  Sun  passes  a 
node  there  must  be  an  eclipse,  and  as  it  passes 
both  nodes  each  year,  it  is  evident  that  there 
must  be  two  solar  eclipses  each  year,  and  it  is 
possible  for  four  to  occur  to  some  parts  of  the 
earth's  surface.  (Fig.  7) 

Lunar  Eclipses.  It  was  noted  by  the  earl- 
iest Astronomers  that  the  Earth  cast  a  shadow, 


—52— 

and  that  as  the  Moon  passed  into  this  shadow 
it  become  eclipsed.  That  lunar  eclipses  only 
occur  occasionally  depends  upon  the  same  gen- 
eral principles  of  solar  eclipses.  The  Earth's 
shadow,  like  the  Sun,  is  in  the  plane  of  the 
ecliptic.  Owing  to  the  great  magnitude  of  the 
Sun,  the  Earth's  shadow  is  much  smaller  at 
the  point  where  the  Moon  passes  it  than  the 
Earth.  (Fig.  8.)  The  Moon  must  therefore 
be  very  near  one  of  its  nodes  at  full  Moon,  or 
it  will  fail  to  strike  the  shadow,  and  will  either 
pass  above  or  below  it.  It  is,  therefore,  evi- 


dent that  lunar  eclipses  are  of  less  frequent 
occurrence  than  solar  eclipses.  A  whole  year 
may  pass  without  there  being  a  lunar  eclipse, 
and  there  never  can  be  more  than  two. 

Total,  Annular  and  Partial.  The  nature  of 
an  eclipse  varies  with  the  relative  position  of 
the  Earth,  Sun  and  Moon.  If  new  Moon  oc- 
curs when  the  Sun  is  at  or  very  near  the  node, 
and  the  Earth  is  in  the  region  of  aphelion, 
and  the  Moon  is  in  the  region  of  perigee,  the 
angular  diameter  of  the  Moon  will  exceed  that 


—53— 

of  the  Sun,  and  the  shadow  of  the  Moon  will 
then  fall  upon  the  Earth,  and  the  whole  disk 
of  the  Sun  will  be  hid;  this  is  called  a  total 
eclipse.  If  a  similar  eclipse  should  take  place 
when  the  Moon  is  in  the  region  of  apogee,  and 
the  Earth  in  the  neighborhood  of  perihelion, 
the  angular  diameter  of  the  Sun  will  exceed 
that  of  the  Moon,  and  the  Moon's  shadow  will 
not  reach  the  Earth,  then  only  a  circular  por- 
tion of  the  Sun  will  be  hid  and  a  ring  of  light 
around  the  edge  of  the  Sun  will  be  visible ;  this 
is  called  an  annular  eclipse.  If  the  Moon  does 
not  pass  centrally  over  the  Sun,  but  a  little 
above  or  below  the  ecliptic,  so  that  only  a  part 
of  the  Sun  is  hid,  it  is  said  to  be  a  partial 
eclipse.  So  with  lunar  eclipses ;  if  the  shadow 
only  strikes  a  portion  of  the  Moon,  it  is  a  par- 
tial eclipse,  but  if  the  whole  disk  of  the  Moon 
is  immersed  in  the  shadow,  it  is  a  total  eclipse. 
As  the  shadow  of  the  Earth  where  the  Moon 
crosses  it  is  larger  than  the  Moon,  a  lunar 
eclipse  cannot  be  annular. 

The  Sun,  and  the  Moon's  Nodes.  There  are 
two  periods  in  each  year  when  the  Sun  passes 
the  Moon's  nodes,  and,  therefore,  eclipses  will 
occur  during  those  seasons.  A  solar  eclipse 
may  occur  eighteen  days  before  and  after  the 
Sun's  passage  through  the  node,  while  that 
for  lunar  eclipses  extends  11%  days  each  side 
of  the  node,  making  a  total  season  for  solar 


eclipses   of   3   days,    and   23    days   for   lunar 
eclipses,  each  time  the  Sun  passes  a  node. 

The  Changes  of  the  Moon's  Nodes.  The 
Moon's  nodes  are  continually  changing  or  fall- 
ing back  to  meet  the  Moon,  so  that  eclipses 
will  occur  on  an  average  of  about  twenty  days 
earlier  each  year.  To  find  the  middle  of  an 
eclipse  season,  or  the  time  the  Sun  passes  a 
node  for  twenty-five  or  thirty  years,  subtract 
19  2-3  days  from  any  of  the  dates  given  herein 
for  the  middle  of  the  eclipse  period  for  each 
subsequent  year.  We  find  for  1881  that  the 
Sun  was  in  the  node  about  June  6,  and,  as  full 
Moon  occurred  June  11,  there  was  a  total 
eclipse  of  the  Moon  on  that  date.  The  Sun 
passed  the  other  node  about  November  25, 
1881,  and  the  new  Moon  occurred  on  November 
21 ;  there  was  an  annular  eclipse  of  the  Sun  at 
that  date.  On  May  17,  1882,  the  Sun  was  in 
the  node  again,  and  as  the  Moon  was  new  on 
that  day,  a  total  eclipse  occurred;  but,  as  new 
Moon  occurred  at  night,  or  when  America  was 
on  the  opposite  side  of  the  Earth  from  the  Sun, 
it  was  invisible  in  this  country.  The  falling 
back  of  the  Moon  nodes  may  be  clearly  illus- 
trated with  the  Tellurian  by  placing  the  nodal 
points  marked  on  the  inclined  disk  in  line  with 
the  Earth  and  Sun  for  any  date,  and  then, 
with  all  the  parts  operating,  move  the  long  arm 
nearly  around  the  Sun  or  within  20  days  of 


—55— 

the  starting  point,  and  the  nodal  points  on  the 
inclined  disk  will  be  found  in  the  same  line  or 
relative  position  toward  the  Sun  as  at  the 
starting  point. 

The  Saros.  The  Moon  will  return  to  the 
same  node  in  27.2  days  and  is  called  the  "  nodal 
revolution  of  the  Moon,"  or  Draconic  month. 
The  other  period  of  29.5  days  is  called  the 
"synodical  revolution "  of  the  Moon.  Now,  the 
curious  consequence  of  these  figures  shows 
that  there  are  242  Draconic  months,  233  Lu- 
nations (New  Moons)  and  19  returns  of  the 
Sun  to  one  and  the  same  node  of  the  Moon  at 
nearly  the  same  time,  and  all  are  accomplished 
in  18  years,  10  days  and  a  few  hours.  That 
is,  if  the  Sun  and  Moon  should  start  together 
from  the  same  node,  they  would  be  found  to- 
gether very  near  the  same  node  in  the  period 
above  mentioned,  and  eclipses  would  occur 
almost,  though  not  quite,  in  the  same  regular 
order  in  about  18  years,  10  days  and  7  hours. 
This  is  the  celebrated  Chaldean  " Saros,"  and 
was  used  by  the  ancients  for  the  prediction  of 
the  eclipses  alike  of  the  Sun  and  Moon,  and 
may  be  used  by  the  modern  as  an  interesting 
and  instructive  pastime. 

The  mechanism  of  the  Tellurian  is  so  timed 
that  it  produces  these  results. 

The  effects  of  the  operation  of  the  "Saros" 
may  be  noticed  in  the  following  two  noteworthy 


—56— 

"Saros"  groups  of  solar  eclipses  during  the 
second  half  of  the  nineteenth  century: 

1842 July    8  1850  August    7 

1860    July  18  1868  August  17 

1878 July  29  1886  August  29 

1896 August    9  1904  ..September    9 

For  a  more  complete  elucidation  of  the  above 
facts,  we  give  in  tabular  form  all  the  eclipses 
of  a  succession  of  half  of  a  "Saros,"  or  nine 
years,  and  thus  show  more  clearly  the  princi- 
ples we  have  endeavored  to  explain. 

Approximate 
Mid-interval. 


1894 — March   21,  eclipse,  Moon.  .  .  . 

April    6,    eclipse,    Sun 

September  15,  eclipse,  Moon.  <    0_    _v_     00!k, 


April    6,    eclipse,    Sun f 

September  29,  eclipse,  Sun"!  }   SePtember 


1895  —  March   11,  eclipse,  Moon.  .  .  . 

Ma™h   J 


.  .  .  .  | 
f 


March  26,  eclipse,  Sun 

August  20,  eclipse,  Sun.  .  .  .  .  J 

September  4,  eclipse,  Moon.  .  V   .  .September  4** 

September  18,  eclipse,  Sun.  .  ) 

1896  —  February    13,   eclipse,    Sun.. 

February    28,  eclipse,    Moon, 

August    9,    eclipse,   Sun  .....  ) 

August  23,  eclipse,  Moon.  .  .  .  f    "  -August    16 

1897  —  February    1,    eclipsie,    Sun  .......  February  1* 

July    29,   eclipse,    Sun  ............  July  29** 


) 

f    ••Febr™ry     20* 


—57— 

1898 — January   7,  eclipse,   Moon.  .  .  )  .January  14* 

January  22,  eclipse,  Sun.  .  .  .  f 

July    3,   eclipse,    Moon )  July     10** 

July  18,  eclipse,  Sun ) 

1898 — December   13,   eclipse,   Sun.  .  J 

December   27,  eclipse,   Moon.   >    ..December   27* 
1899 — January  11,  eclipse,  Sun.  .  .  .  ) 

June    8,   eclipse,   Sun I  Juiie    ^^ 

June   23,  eclipse,   Moon } 

December   2,   eclipse,   Sun. . .  )         .December   9* 
December   16,  eclipse,  Moon.  ) 

1900 — May    28,    eclipse,    Sun )  June    5<e>|t 

June   13,   eclipse,  Moon ) 

November   22,  eclipse,   Sun.  .        .November     22* 

1901 — May    3,    eclipse,    Moon )     .May  10** 

May    18,    eclipse,    Sun ) 

October    27,   eclipse,    Moon.  .  ) 

November   11,  eclipse,  Sun..}     •••November  3* 

1902 — April   8,   eclipse,   Sun | 

April   22,  eclipse,  Moon >    April  22** 

May   7,  eclipse,  Sun ) 

October  17,  eclipse,  Moon.  .  ) 

October  31,  eclipse,   Sun.  .  .  .  f   '  '  '  -Oct°ber  24* 

One  *  denotes  the  ascending  node,  and  two 
*  denotes  the  descending  node.    We  give  here 
some  recent  eclipses : 


1904 — March  17,  annual  eclipse  of  the  Sun** 
September  9,  total  eclipse  of  the  Sun. 


—58— 

1906 — February  9,  total  eclipse  of  the  Moon. 
February  23,  partial  eclipse  of  the  Sun. 
July  21,  partial  eclipse  of  the  Sun.* 
August  4,  total  eclipse  of  the  Moon.** 
August  19-20,  partial  eclipse  of  the  Sun.* 

1909— June  3,  total  eclipse  of  the  Moon.** 
June  17,  partial  eclipse  of  the  Moon. 
November  27,  total  eclipse  of  the  Moon. 
December  12,  partial  eclipse  of  Sun.*4 

1910 — May  9,  total  eclipse  of  the  Sun.* 

May  23-24,  total  eclipse  of  the  Moon.** 
November  2,  partial  eclipse  of  the  Sun.** 
November  16,  total  eclipse  of  the  Moon. 

One  *  denotes  the  ascending  node,  and  two  * 
denote  the  descending  node. 

To  Adjust  the  Mo-on's  Nodes  to  Show  the 
Eclipses  With  the  Tellurian. . .  Throw  ' '  out  of 
gear.'7  The  inclined  disk  on  which  the  Moon's 
support  travels  causing  the  Moon  to  rise  and 
fall  in  its  orbit,  has  two  points  marked  upon 
it  half  way  between  the  highest  and  lowest 
points.  These  points  are  intended  to  indicate 
the  Moon's  node;  that  is,  when  the  small  trav- 
eler that  supports  the  Moon  is  at  these  points, 
the  Moon  is  in  its  node.  The  one  where  the 
Moon  is  rising  is  called  the  ascending  node, 
and  the  other,  where  the  Moon  is  passing 
downward,  is  called  the  descending  node.  De- 
termine from  an  almanac,  astronomy  or  ap- 
pended table  of  the  eclipses  the  time  of  an 


Plate   IV. 
Eclipse  of  the  Sun. 


57 


—59— 

eclipse  of  the  Sun  or  Moon,  and  whether  at  the 
ascending  or  descending  node,  and  bring  the 
node  in  a  line  with  the  long  arm,  the  arm  be- 
ing over  the  date  indicated  for  the  eclipse  of 
the  Sun.  The  Moon  should  be  in  a  line  be- 
tween the  Earth  and  Sun,  or  new  Moon.  If  a 
total  eclipse,  the  Moon  will  be  in  a  line  with 
the  node,  and  between  the  center  of  the  Earth 
and  the  center  of  the  Sun,  or  in  the  plane  of 
the  ecliptic.  If  a  partial  eclipse,  and  visible 
in  the  Northern  Hemisphere,  the  nodal  point 
should  be  moved  back  a  little  so  the  Moon  will 
be  partially  above  the  plane  of  the  ecliptic.  If 
the  eclipse  is  visible  in  the  Southern  Hemi- 
sphere, the  nodal  points  should  be  moved  for- 
ward a  little  so  the  Moon  would  be  partially 
below  the  plane  of  the  ecliptic.  These  same 
conditions  apply  to  the  eclipses  of  the  Moon, 
only  the  Moon  should  be  in  opposition,  or  full 
Moon,  where  the  shadow  of  the  Earth  would 
fall  upon  it.  Having  thus  adjusted  the  mech- 
anism and  "thrown  in  gear"  the  operation  of 
the  Tellurian  will  readily  show  the  cause  and 
dates  of  the  eclipse  of  the  Sun  and  Moon  for 
a  number  of  years. 

^Third  Motion  of  the  Earth  and  Lunar  Orbit. 
It  is  in  consequence  of  the  mutual  gravitation 
of  all  the  several  parts  of  matter,  which  the 
Newtonian  law  supposes,  and  the  third  law, 
that  action  is  equal  to  reaction,  and  in  oppo- 


—60— 

site  direction,  that  the  Earth  and  the  Moon 
revolve  about  their  common  center  of  gravity 
in  their  monthly  orbit,  and  continue  to  cir- 
culate, without  parting  company,  in  a  greater 
annual  orbit  around  the  sun.  We  may  con- 
ceive this  motion  by  connecting  two  unequal 
balls  by  a  short  stick,  which  to  their  common 
center  of  gravity  is  suspended  by  a  long  string 
and  made  to  gyrate  conically  round  a  point 
vertically  below  that  of  suspension.  Their 
joint  system  will  circulate  as  one  pendulous 
mass  about  this  imaginary  center,  while  yet 
they  may  go  on  circulating  round  each  other 
in  subordinate  gyrations,  as  if  the  stick  were 
quite  free  from  any  such  tie,  and  merely  hurled 
through  the  air. 

If  the  Earth  alone,  and  not  the  Moon,  gravi- 
tated to  the  Sun,  it  would  be  dragged  away 
and  leave  the  Moon  behind,  and  vice  versa; 
but,  acting  on  both,  they  continue  together 
under  its  attraction,  just  as  the  loose  parts  of 
the  Earth's  surface  continue  to  rest  upon  it. 
It  is,  then,  in  strictness  not  the  Earth  or  the 
Moon  which  describes  an  ellipse  around  the 
Sun,  but  their  common  center  of  gravity.  The 
effect  is  to  produce  a  small,  but  very  per- 
ceptible monthly  equation  in  the  Sun's  appar- 
ent motion  as  seen  from  the  Earth,  which  is 
always  taken  into  account  in  calculating  the 
Sun's  place.  The  Moon's  actual  path  in  its 


—61— 


Partial.  Annular. 

Fig.   10. 

compound  orbit  around  the  Earth  and  Sun  is 
an  epicycloidal  curve,  intersecting  the  orbit  of 
the  Earth  twice  every  lunar  month,  and  alter- 
nately within  and  without  it.  But  as  there 
are  not  more  than  twelve  such  months  in  the 
year,  and  as  the  total  departure  of  the  Moon 
from  it  either  way  does  not  exceed  l-400th 
part  of  the  radius,  this  amounts  only  to  a  slight 
undulation  upon  the  Earth's  ellipse,  so  slight, 
indeed,  that  if  drawn  in  true  proportion,  on  a 
large  sheet  of  paper,  no  eye,  unaided  by  meas- 
urement with  compasses,  would  detect  it.  The 
real  orbit  of  the  Moon  is  everywhere  concave 
towards  the  Sun. 

The  motions  of  the  Earth  and  Moon  about 
their  common  center  of  gravity  are  so  per- 
fectly represented  in  the  Tellurian,  that  by 
simply  observing  it,  they  can  readily  be  under- 
stood. These  motions  play  a  very  important 
part  in  the  causes  of  the  tides  where  they  will 
again  be  considered. 


The  Tides 


Owing  to  the  erroneous  theories  generally 
given  in  text-books,  the  teacher  as  well  as  the 
learner  has  hitherto  experienced  great  diffi- 
culty in  clearly  comprehending  the  causes  of 
the  tides.  The  old  theory  fails  to  give  satis- 
factory explanation  of  the  cause  of  the  tides 
on  the  side  of  the  Earth  most  remote  from  the 
Sun  and  Moon.  According  to  the  usually  as- 
cribed cause  in  our  text-books,  the  side  of  the 
Earth  farthest  from  the  Sun  or  Moon  is  less 
influenced  by  the  attractive  force  of  these  bod- 
ies, and  consequently  the  solid  portion  of  the 
Earth  is  drawn  away,  thus  leaving  the  water 
bulged  out  behind,  causing  a  tide.  That  such 
would  be  the  fact  is  contrary  to  all  known 
laws  of  physics.  The  attractive  influence  of 
the  Sun  or  Moon  will  be  less  on  the  side  of 
the  Earth  most  remote  from  it,  yet  the  gravi- 
tation of  the  Earth  acting  in  the  same  line 
with  those  bodies,  the  water  would  be  drawn 
more  closely  to  the  Earth  in  that  part,  if  no 
other  influence  existed.  That  the  attractive 
force  is  greatest  at  this  point  has  been  proved 
by  experiment,  it  having  been  ascertained  by 


—63— 

actual  test  that  a  body  weighs  more  at  mid- 
night than  at  any  other  hour. 

If  the  old  theory  were  correct,  the  weight 
of  a  body  would  be  less  at  midnight  than  at 
any  other  hour,  since  at  that  hour  the  object 
is  on  the  opposite  side  of  the  Earth  from  the 
Sun.  Surely,  if  it  were  the  absence  of  the 
attractive  force  which  caused  the  water  to 
bulge  out  at  that  point,  the  absence  of  the 
same  force  would  be  manifest  in  lessening  the 
weight  of  an  object  at  the  same  place.  In  ac- 
cordance with  the  fact  that  an  object  weighs 
most  when  on  the  side  of  the  Earth  most  re- 
mjote  from  the  Sun,  it  follows  as  a  necessary 
consequence  that  when  the  object  is  on  the 
side  of  the  Earth  nearest  the  Sun  at  mid- 
day, it  would  likewise  decrease  in  weight. 

A  close  examination  of  the  movements  of 
the  Tellurian  and  a  knowledge  of  the  laws  of 
planetary  motion  will  present  clearly  to  the 
mind  a  satisfactory  theory  of  the  tides,  based 
upon  known  laws.  If  we  attach  a  ball  to  the 
end  of  a  string  and  revolve  it  around  the  hand, 
it  will  have  a  tendency  to  fly  off  at  a  tangent, 
or  at  a  right  angle  to  the  string,  and  the  faster 
it  revolves  the  greater  will  be  the  tension  on 
the  string.  This  then,  will  illustrate  the  two 
great  forces  of  planetary  motion.  The  ten- 
dency that  the  ball,  or  body,  will  have  to  fly 
off  is  called  the  centrifugal  force,  and  that 


which  binds  it  to  the  center  around  which  it 
revolves  is  called  the  centripetal  force.  If 
the  ball  suspended  by  the  string  be  dipped  in 
water  and  then  removed,  the  water  adhering 
to  it  will  run  to  the  lower  portion  of  the  ball 
by  the  force  of  gravity  of  the  Earth  acting 
upon  it.  Now,  if  we  revolve  the  ball  attached 
to  the  string,  the  water  still  adhering  will  fly 
off  from  the  side  opposite  the  string,  that  be- 
ing the  point  on  the  ball  farthest  from  the 
hand.  In  the  movements  of  all  heavenly  bodies 
the  centrifugal  and  centripetal  forces  are  pre- 
cisely equal,  as  may  be  illustrated  by  the 
string.  The  general  law  of  matter,  that  all 
bodies  attract  all  others  in  proportion  to  their 
mass,  and  inversely  as  the  square  of  the  dis- 
tance increases,  should  be  considered.  We  are 
now  ready  to  understand  the  tides. 

Solar  Tides.  The  Earth  revolves  on  its  axis 
in  twenty-four  hours,  and  thus  there  are  two 
solar  tides,  or  tides  caused  by  the  Sun,  each 
day,  one  beneath  the  Sun,  and  the  other  on  the 
side  of  the  Earth  most  remote. 

These  are  constant  and  always  remain  in  the 
same  relative  position  to  the  Sun,  thus  always 
keeping  an  elevation  of  water  directly  under 
the  Sun,  and  one  on  the  side  of  the  Earth  op- 
posite. Each  particular  portion  of  the  Earth 
passes  these  two  forces  daily,  and  as  the  seas 
pass  them,  a  tide  is  caused  by  the  water  being 


—65— 

raised  above  its  natural  level  on  the  Earth's 
surface.  To  the  observer,  who  is  necessarily 
moving  with  the  Earth's  revolution,  these  tides 
appear  to  be  following  each  other  around  the 
globe,  when,  in  fact,  they  always  keep  the  same 
relative  position  to  the  Sun,  and  it  is  the  re- 
volving of  the  Earth  on  its  axis  that  causes 
objects  on  its  surface  to  pass  the  solar  tides. 
On  the  portion  of  the  earth  nearest  the  Sun 
the  water  is  drawn  out  or  piled  up  by  the 
gravitating  force  lodged  in  the  central  orb,  as 
the  particles  of  water  move  very  easily  among 
each  other,  and  yield  more  readily  to  the  at- 
tractive influence  than  do  the  solid  portions  of 
the  Earth.  The  Solar  tide  most  remote  from 
the  Sun  is  caused  by  the  centrifugal  force  pro- 
duced by  the  revolution  of  the  Earth  around 
the  Sun.  Thus,  the  bulging  out  of  the  water 
on  one  side  is  caused  by  the  centripetal  force, 
and  on  the  other  side  by  the  centrifugal  force. 
It  must  be  remembered  that  every  particle  of 
the  Earth  feels  the  effect  of  these  two  forces 
in  its  orbital  motions,  but  the  surface  of  the 
Earth  next  to  the  Sun,  being  nearest,  feels  the 
centripetal  force  in  excess  of  the  centrifugal, 
and  the  surface  most  remote  from  the  Sun 
feels  the  centrifugal  force  in  excess  of  the 
centripetal.  The  effect  is  seen  in  the  tide.  At 
the  center  of  the  Earth  these  two  forces  are 
exactly  equal.  Again,  the  side  of  the  Earth 


—66— 

most  remote  from  the  Sun  is  8,000  miles  far- 
ther from  the  Sun  than  the  side  turned  toward 
it,  and,  consequently,  the  farther  side  moves 
more  rapidly,  producing  greater  centrifugal 
force. 

Lunar  Tides.  We  have,  so  far,  spoken  only 
of  the  solar  tide.  By  far  the  greater  and  more 
sensible  tide  is  caused  by  the  Moon.  Although 
the  Sun  is  vastly  larger  than  the  Moon,  yet  its 
effect  in  producing  the  tide  is  much  less  than 
that  of  the  latter  body,  the  ratio  being  about 
one  to  three.  That  is,  while  the  Sun  raises 
the  tide  one  foot,  the  Moon  will  raise  it  three 
feet.  This  is  owing  to  the  close  proximity  of 
the  Earth  and  Moon.  The  Earth,  as  a  whole, 
feels  the  gravitating  of  the  Earth  and  Moon. 
The  Earth,  as  a  whole,  feels  the  gravitating 
influence  of  the  Sun  much  more  than  that  of 
the  Moon,  but  upon  a  particular  portion  of  the 
Earth  the  influence  of  the  Moon  is  greater. 

There  are  two  lunar  tides,  one  on  the  side 
of  the  Earth  facing  the  Moon,  caused  by  the 
centripetal  force  of  the  Moon,  and  the  other 
on  the  side  of  the  Earth  most  remote  from  the 
Moon,  caused  by  the  centrifugal  force  pro- 
duced by  the  Earth  revolving  around  the  com- 
mon center  of  gravity  of  these  two  bodies.  The 
daily  and  yearly  motions  of  the  Earth  are  gen- 
erally understood,  and,  although  we  are  in  the 
habit  of  considering  the  Moon  as  simply  re- 


—67— 

volving  around  the  Earth,  it  must  be  remem- 
bered that  the  attraction  is  mutual;  that  both 
bodies  describe  orbits  about  their  common  cen- 
ter of  gravity,  and  that  while  the  Moon  obeys 
the  attraction  of  the  Earth,  the  latter  equally 
follows  that  of  the  former,  by  which  it  is  at 
every  instant  drawn  from  the  path  it  would 
pursue  if  that  influence  did  not  exist.  This 
motion  is  very  perfectly  shown  by  the  Tellu- 
rian. The  lunar  tides  traverse  the  globe  with 
the  Moon,  and  as  to  time  differ  from  the  solar 
tides.  The  centripetal  and  centrifugal  forces, 
acting  in  oposite  directions,  will  also  cause 
tide  waves  on  opposite  sides  of  the  Earth,  and, 
as  the  forces  are  always  equal,  the  tides  pro- 
duced must  also  be  equal.  The  Earth  and 
Moon  are  comparatively  close  to  each  other, 
and  the  Earth  is  much  larger,  and  consequent- 
ly the  orbit  of  the  Earth  around  the  center  of 
gravity  will  be  very  small;  yet  the  centrifugal 
force  does  not  depend  altogether  upon  the  ve- 
locity with  which  a  body  moves,  but  upon  the 
size  of  the  curve  described  by  the  body.  It 
will  be  observed  that  the  Earth  in  its  lunar 
motion  turns  very  short  corners,  as  it  were, 
and  thus  there  will  be  a  great  tendency  in 
every  part  of  the  Earth's  lunar  orbit  to  throw 
off,  or  bulge  it  out,  as  in  the  tides. 

Spring  Tide.     If  the  Moon  is  in  conjunction, 
as  at  new  Moon,  the  centripetal  forces  of  the 


—68— 

Sun  and  Moon  act  together,  and  the  solar  and 
lunar  tides  will  occur  at  the  same  time,  and, 
as  shown  in  figure  1,  a  large  tide  will  be  the 
result.  On  the  side  of  the  Earth  turned  away 
from  these  bodies,  an  equal  tide  will  occur;  at 
that  point  the  Earth  feels  the  centrifugal  force 
produced  by  its  revolutions  around  the  Sun, 
and  its  revolutions  around  the  common  center 
of  gravity.  The;se  two  forces  act  in  one  and 
the  same  straight  line.  Now  let  us  place  the 
Moon  and  Sun  so  as  to  be  in  opposition,  or 
full  Moon,  and  again  there  will  be  a  large  tide 
on  the  side  of  the  Earth  facing  the  Sun,  caused 
by  the  centrifugal  forces  generated  by  the  rev- 
olution of  the  Earth  around  the  common  center 
of  gravity,  and  centripetal  force  of  the  Sun 
acting  together.  On  the  side  of  the  Earth  fac- 
ing the  Moon  the  centripetal  force  of  the  Moon 
will  act  in  conjunction  with  the  centrifugal  in- 
fluence produced  by  the  revolution  of  the  Earth 
around  the  Sun,  and  thus  there  will  be  equal 
tides  on  opposite  sides  of  the  Earth.  These 
high  tides  are  denominated  Spring  Tides. 

Neap  Tide.  At  first  and  third  quarter,  or 
when  the  Moon  is  in  quadrature,  as  shown  in 
Figure  2,  the  centripetal  force  of  the  Moon  will 
act  at  right  angles  with  the  centripetal  force 
of  the  Sun  and  the  centrifugal  force  produced 
by  the  Earth  revolving  around  the  common 
center  of  gravity  of  the  Earth  and  Moon,  and 


—69— 

its  revolutions  around  the  Sun,  likewise  act  at 
right  angles  to  each  other,  and  we  will  have 
the  phenomena  of  the  solar  and  lunar  tides 
about  90°  apart,  the  solar  tide  being  the  smal- 
ler, and  the  lunar  tide  the  larger.  These  are 
called  Neap  Tides.  The  tide  now  will  neither 
rise  so  high,  nor  fall  so  low  as  at  new  or  full 
Moon.  The  solar  tides  occur  at  regular  inter- 
vals of  twelve  hours,  but  the  Moon  revolving 
eastward  comes  to  a  given  meridian  later  and 
later  each  day  and  thus  there  will  be  a  lunar 
tide  on  an  average  every  twelve  hours,  and 
twenty-five  minutes  or  fifty  minutes  later  each 
day.  The  ponderous  weight  of  such  a  great 
mass  of  water  as  constitutes  a  tide  is  not 
suddenly  raised  by  the  Moon's  attraction,  but 
yields  slowly  to  the  unseen  force,  so  that  the 
greatest  effect  is  noticed  after  the  Moon  has 
passed.  For  this  reason  the  highest  point  of 
the  tide  is,  in  the  open  ocean,  45°  behind  or 
oast  of  that  body. 

The  Heights1  of  Tides  in  Different  Parts  of 
the  World.  The  time  is  often  essentially  var 
ied  by  local  influences  as  the  direction  of  coasts 
and  the  peculiar  shape  of  bays  and  mouths  of 
rivers.  If  a  place  is  situated  on  a  large  bay, 
with  but  a  narrow  strait  connecting  it  with 
the  sea,  the  tide  will  be  longer  in  rising,  as  the 
bay  has  to  fill  up  through  a  narrow  gate. 
Hence  it  is  that  at  New  York  high  tide  usually 


—70— 

occurs  eight  or  nine  hours  after  the  Moon  has 
passed  the  meridian.  There  are  some  very 
interesting  phenomena  to  be  noticed  in  the 
tide  in  Puget  Sound,  owing  to  the  peculiar 
form  and  size  of  that  body  of  water  and  its 
connection  with  the  ocean  by  the  Straits  of 
Juan  de  Fuca.  At  Olympia,  the  extreme  south- 
ern point  of  the  Sound,  the  tide  varies  much, 
both  as  to  height  and  time  from  the  tide  on  the 
main  coast  near  by.  The  tidal  wave  comes 
westward  at  the  rate  of  about  1,000  miles  per 
hour;  therefore,  in  striking  the  eastern  coast 
of  continents  the  water  rushes  far  up  into  bays 
and  rivers,  and  oft-times  with  great  violence, 
producing  wonderful  high  tides.  The  water 
from  the  Atlantic  Ocean  is  thus  swept  into 
the  Gulf  of  Mexico,  and  raises  a  tide  on  the 
coast  of  Central  America  to  the  height  of 
eighteen  feet.  The  mjouth  of  the  Gulf  is  wide, 
and  so  shaped  as  to  gather  the  water  from  a 
large  part  of  the  ocean,  and  thus  concentrate 
the  tide,  as  it  were,  in  comparatively  narrow 
limits  at  the  western  extremity  of  the  Gulf. 
,This  phenomena  is  manifested  more  in  the 
Bay  of  Fundy  than  in  any  other  place  on  the 
globe,  at  which  place  it  rises  at  times  to  the 
enormous  height  of  seventy  feet.  By  observ- 
ing the  map  of  the  Bay  of  Fundy  and  its  sur- 
roundings, and  considering  the  shallowness  of 
the  Atlantic  Ocean  beyond,  we  may  readily 


—71— 

understand  why  the  water  would  rush  up  the 
Bay  with  such  force.  The  further  up  a  bay 
or  river,  the  later  the  tide  will  occur.  At  Cape 
Good  Hope  there  is  scarcely  any  perceptible 
tide,  owing  to  the  fact  that  as  the  water  rushes 
against  the  lower  portion  of  the  eastern  coast 
of  Africa,  it  is,  by  the  angle  of  the  coast  line, 
caused  to  flow  down  to  the  Cape  by  its  own 
force.  It  reaches  the  Cape  just  as  the  water 
in  that  vicinity  is  going  out  so  the  change  is 
not  noticed  and  the  water  appears  to  remain 
unmoved  at  that  particular  place. 

The  Height  of  Tides  at  Different  Seasons  of 
the  Year.  At  certain  seasons  of  the  year 
the  tides  occurring  at  night  and  during  the 
day  attain  different  heights — the  greatest  dif- 
ference being  in  June  and  December.  In  March 
and  September  there  will  be  no  perceptible 
difference  between  the  day  and  night  tides. 
This  phenomena  is  occasioned  by  the  inclina- 
tion of  the  Earth  to  the  plane  of  the  ecliptic. 
The  tides  must  necessarily  be  under  the  lift- 
ing forces  and  directly  opposite  to  those  forces. 
If  we  place  the  Moon  in  conjunction  with  the 
Sun,  in  the  beginning  of  winter,  the  lifting 
forces  will  be  south  of  the  equator,  and  the 
centrifugal  force  will  be  north  of  the  equator 
on  the  opposite  side  from  the  centripetal 
forces.  Thus  in  the  Northern  and  Southern 
Hemispheres  we  will  have  each  alternate  tide 


—72— 

higher.  Now,  change  the  bodies  to  like  posi- 
tion at  the  beginning  of  summer,  and  just  the 
opposite  will  be  the  result,  and  again  each  al- 
ternate tide  will  be  higher.  The  same  may  be 
shown  by  placing  the  bodies  in  opposition. 
Thus  the  pupil  may  readily  see  the  cause  of 
this  phenomenon.  When  the  Moon  is  in  peri- 
gee the  tide  will  be  somewhat  increased,  owing 
to  the  nearness  of  the  bodies  at  that  time. 
Likewise,  when  the  Moon  is  in  apogee,  the 
tide  will  be  slightly  reduced.  The  character 
of  tides  are  also  affected  by  the  winds.  Strong- 
winds  may  either  retard  or  hasten  the  move- 
ments of  the  water,  or  may  increase  or  dimin- 
ish the  height  of  the  tide. 

There  is  no  perceptible  tide  in  the  Great 
Lakes,  owing  to  the  small  compass  and  shal- 
lowness  of  the  water. 

We  have  spoken  in  this  article  of  the  in- 
creased weight  of  an  object  on  that  part  of 
the  earth  most  remote  from  the  Sun,  but  this 
will  in  no  wise  conflict  with  the  centrifugal 
force  in  producing  the  tide,  as  this  force  acts 
as  a  tangent  to  the  orbit,  or  at  right  angles 
to  the  radius-vector. 


Time 

For  the  convenience  of  civil  life,  a  specific 
measurement  of  time  is  essential.  The  great 
standard  is  the  revolution  of  the  Earth  on  its 
axis  which  is  always  the  same.  The  transit  of 
a  heavenly  body  is  the  moment  it  is  on  the 
meridian  of  the  observer;  when  it  is  on  the 
meridian  nearest  the  observer,  it  is  the  upper 
transit;  when  on  the  one  most  remote,  the 
lower  transit.  The  period  of  the  revolution 
of  the  Earth  on  its  axis  is  23  houis  and  56 
minutes,  the  time  between  two  successive  up- 
per transits  of  a  star,  which  is  called  siderial 
time.  This  is  always  used  for  astronomical 
purposes,  and  in  hours  is  numbered  from  1  to 
24.  The  right  ascension,  or  siderial  time  of 
the  Earth  and  Sun,  is  marked  upon  the  chart 
for  any  day  in  the  year.  On  March  21  siderial 
noon  corresponds  with  solar  noon,  and  on  Sep- 
tember 23  siderial  noon  to  midnight. 

The  Earth  in  its  annual  motion  around 
the  ecliptic  continually  changes  its  longtitude, 
at  the  rate  of  about  1°  each  day;  it  must,  there- 
fore, make  1°  more  than  a  revolution  on  its 
axis  between  two  successive  upper  transits  of 
the  Sun.  This  is  called  solar,  or  Sun,  time. 
The  difference,  then,  between,  siderial  and  Sun 
time  is  about  four  minutes ;  that  is,  if  the  Sun 


—74— 

and  a  star  should  make  their  upper  transits 
at  the  same  moment,  the  star  would  return  to 
the  same  meridian  about  four  minutes  before 
the  Sun.  In  a  year  the  star  would  make  one 
more  upper  transit  than  the  Sun,  or,  in  other 
words  the  siderial  days  in  a  year  are  one  more 
than  the  solar  days. 

The  Earth  moves  faster  in  its  orbit  when 
in  perihelion  than  when  at  aphelion  and  thus 
varies  the  rate  at  which  the  Sun  and  Earth 
change  their  right  ascension.  The  Sun  would, 
therefore,  make  its  upper  transit  at  irregular 
intervals.  As  it  will  be  seen,  when  the  Earth 
is  changing  its  right  ascension  faster,  as  at 
perihelion,  it  must  be  a  little  more  than 
twenty-four  hours  between  two  successive 
upper  transits  of  the  Sun,  and  when  it  is  in 
another  part  the  time  between  two  upper 
transits  of  the  Sun  will  be  a  little  less  than 
twenty-four  hours.  At  the  equinox  the  Sun 
moves  obliquely  to  the  meridian,  and  also 
varies  the  solar  noon.  This  time,  as  measured 
by  the  Sun,  is  apparent  time.  Mean  time  is 
the  average  of  all  the  solar  days  in  the  year. 
This  is  the  civil  day  of  twenty-four  hours,  and 
begins  at  midnight,  or  when  the  Sun  is  on  the 
lower  transit.  It  is  divided  into  two  periods 
of  twelve  hours  each,  beginning  at  midnight 
and  noon.  The  interval  between  mean  and 
apparent  time  is  called  equation  of  time.  The 


—75— 

equation  of  time  must  sometimes  be  added  to 
and  sometimes  subtracted  from,  apparent  time, 
to  give  the  mean.  When  the  Sun  is  "slow"  it 
must  be  added  and  when  "fast"  it  must  be 
subtracted  to  give  the  mean.  The  greatest  ad- 
ditive value  is  about  fifteen  minutes,  February 
11,  and  the  greatest  subtractive  value  is  about 
sixteen  minutes,  November  3.  The  equation  of 
time  is  0  four  times  a  year — April  15,  June  15, 
September  1  and  December  24.  The  number 
of  minutes  the  Sun  is  "slow"  or  "fast"  for 
any  day  in  the  year  is  marked  on  the  chart  on 
the  Tellurian,  and  the  positions  of  the  Earth 
relative  to  the  Sun  should  be  noticed  in  con- 
nection with  the  above  explanations,  when  it 
will  become  very  simple.  As  the  Earth  re- 
volves to  the  east  any  place  east  of  a  given 
meridian  must  be  later,  and  west,  earlier. 

The  hour  band  is  numbered  from  one  to 
twelve,  and  then  the  same  repeated,  so  one 
twelve  will  show  the  noon  meridian  and  the 
other  midnight.  When  it  is  desired  to  find  the 
difference  in  longtitude  or  time  between  any 
two  given  places  bring  the  meridian  passing 
through  one  of  the  points  to  the  noon  twelve 
and  notice  where  the  meridian  passing  through 
the  other  point  strikes  the  hour  band,  which 
will  show  the  time.  All  problems  in  Longti- 
tude and  Time  can  thus  be  solved  and  simpli- 
fied. 


Precessson  of  the  Equinoxes 


By  comparing  the  observations  of  the  pres- 
ent with  those  mapped  out  by  the  astronomers 
of  the  last  2,000  years,  it  is  found  that  the 
equinoxes  are  slightly  shifting  their  places 
among  the  fixed  stars ;  the  change  being  about 
1°  towards  the  west  in  about  seventy  years. 
But  this  change  is  so  slow  that  it  is  only  by 
the  refined  instrument  of  modern  times  that 
it  can  be  accurately  determined.  It  will  be 
noticed  that  the  equinoxes  are  90°  from  the 
poles,  and  a  change  in  the  equinoxes  must 
necessarily  be  produced  by  a  change  in  the  di- 
rection of  the  poles.  Precession  is  really  pro- 
duced by  a  very  slow  motion  of  the  North  Pole 
of  the  Earth  around  the  pole  of  the  ecliptic, 
requiring  nearly  26,000  years  for  the  pole  to 
be  carried  all  the  way  around,  the  motion  be- 
ing in  an  opposite  direction  to  that  of  the 
Earth  around  the  Sun.  This  motion  is  due 
mainly  to  the  great  attractive  force  of  the  Sun 
and  Moon  upon  the  protuberance  of  the 
Earth's  equator  and  the  centrifugal  force  of 
the  Earth.  At  present  the  North  Pole  of  the 
Earth  has  its  greatest  inclination  from  the 
Sun,  in  that  part  of  the  ecliptic  denoted  by  the 


—77— 

winter  solstice,  and  is  directed  very  nearly  to- 
ward the  pole  star.  As  the  North  Pole  swings 
to  the  right  the  Sun  will  appear  in  the  equi- 
noxian  points  about  twenty  minutes  earlier 
each  year.  At  this  rate,  in  about  6,500  years 
the  equinoxes  will  fall  back  in  reference  to  the 
fixed  stars  to  the  present  solsticial  points  and 
the  solsticial  points  to  the  present  position  of 
the  equinoxes.  That  is,  the  North  Pole  will 
have  its  greatest  inclination  from  the  Sun  at 
that  point  that  now  marks  the  autumnal  equi- 
nox. In  about  6,500  years  more  the  position 
of  the  solsticial  and  equinoxial  points  will  be 
reversed  and  the  North  Pole  will  be  directed 
about  46°  from  the  present  pole  star,  and  so 
on,  in  a  little  less  than  26,000  years  the  pole 
will  have  returned  to  its  present  position.  The 
return  of  the  Sun  in  reference  to  a  fixed  star 
is  the  siderial  year  and  its  return  to  the  same 
equinox  is  called  the  tropical  or  equinoxial 
year.  Their  exact  lengths  are : 

Days.     Hours.     Min.     Sec. 
Siderial  Year    ....   365  6  9  9 

Tropical  Year  ....   365  5          48          46 

The  latter  is  used  in  the  calendar  as  the  re- 
turn of  the  seasons  depends  upon  it.  In  ex- 
plaining the  above  with  the  Tellurian,  move 
the  Earth  around  in  its  orbit  a  number  of 
times  and  the  change  in  the  direction  of  the 


—78— 

poles  will  be  observed,  or  throw  the  mechan- 
ism "out  of  gear"  when  at  the  winter  solstice, 
December  21,  and  move  the  long  arm  back- 
ward slightly  or  as  much  as  desired  which  will 
illustrate  plainly  the  change  of  the  direction 
of  the  Earth  axis  and  the  consequent  preces- 
sion of  the  equinoxes'. 


i 


The  Solar  System 


Our  Solar  System  is  composed  of  the  Sun, 
the  great  central  luminary,  eight  primary 
planets,  twenty  moons,  about  200  known  aste- 
roids and  a  number  of  comets  and  meteors. 
The  Sun  is  in  the  center  of  the  system,  around 
which  all  the  bodies  revolve  in  elliptical  or- 
bits. It  is  860,000  miles  in  diameter  with  a 
density  about  one-fourth  that  of  the  Earth. 
The  Sun  is  the  source  of  all  the  light  and  heat 
of  the  Solar  System  except  the  dim  twinkling 
that  come  from  the  far  distant  stars.  The 
Sun  is  a  molten  mass  of  similar  composition 
to  our  Earth,  and  revolves  on  its  axis  in  about 
twenty-six  days.  The  first  planet  from  the 
Sun  is  Mercury,  35,750,000  miles  distant,  and 
is  about  2,992  miles  in  diameter  and  makes  a 
revolution  around  the  Sun  in  87.97  days.  The 
second  planet,  Venus,  makes  a  revolution 
around  the  Sun  in  224.7  days,  at  a  distance  of 
66,750,000  miles  and  is  7,660  miles  in  diameter. 
The  third  planet  in  order  is  our  Earth,  at  a 
mean  distance  of  92,330,000  miles.  It  makes 
a  complete  revolution  in  365  days,  6  hours,  9 
minutes,  and  moves  in  its  orbit  at  the  rate  of 
68,000  miles  per  hour,  or  nearly  19  miles  per 


—80— 

second.  Mars,  the  fourth  planet,  makes  a  rev- 
olution around  the  Sun  in  about  687  days  at 
a  mean  distance  of  141,999,000  miles  and  is 
4,211  miles  in  diameter.  It  has  two  satellites, 
which  revolve  very  rapidly  around  the  planet, 
owing  to  their  close  proximity.  Next  beyond 
Mars  is  the  region  of  asteroids,  a  large  col- 
lection of  small  planets  varying  in  size  from 
a  few  miles  to  100  miles  in  diameter.  There 
have  been  about  300  discovered  and  named. 
The  fifth  planet  is  the  great  Jupiter,  86,000 
miles  in  diameter.  It  makes  a  revolution 
around  the  Sun  in  11.86  years,  at  a  mean  dis- 
tance of  480,000,000  miles.  Around  this  planet 
revolve  four  satellites  at  distances  from  260,- 
000  miles  to  over  1,000,000  miles  from  it.  At 
certain  seasons  this  planet,  like  Venus  and 
Mars,  shines  with  great  brilliancy.  Saturn  is 
the  sixth  in  order  of  distance  from  the  Sun, 
around  which  it  revolves  in  29y2  years,  at  a 
mean  distance  of  about  880,000,000  miles,  and 
is  70,500  miles  in  diameter.  It  has  eight  moons 
or  satellites  revolving  around  it.  Two  huge 
rings,  a  hundred  miles  in  thickness,  girdle  this 
planet,  the  larger  having  an  exterior  diameter 
out  of  169,000  miles.  The  seventh  planet  is 
Uranus,  at  a  mean  distance  of  1,771,000,000 
miles  from  the  Sun.  It  is  31,700  miles  in  di- 
ameter and  makes  a  revolution  in  84  years, 
being  accompanied  by  four  satellites.  At  a 


—81— 

distance  of  2,775,000,000  miles  from  the  cen- 
tral orb  rolls  the  farthest  planet  of  the  sys- 
tem, Neptune.  It  makes  a  revolution  in  about 
164%  years,  is  34,500  miles  in  diameter  and 
is  accompanied  by  one  satellite. 

A  number  of  comets  revolve  around  the  Sun 
in  very  eccentric  orbits  and  many  pass  far  be- 
yond the  orbit  of  Neptune. 


Glossary  of  Technical  Terms  Used 
in  this  Book 


Alteration  (a  wandering  away).  Generally 
applied  to  a  real  or  apparent  deviation  of  the 
course  of  a  ray  of  light. 

Altitude.  The  apparent  angular  elevation 
of  a  body  above  the  horizon,  usually  expressed 
in  degrees  and  minutes.  At  the  horizon  the 
altitude  is  zero;  at  the  zenith  it  is  90°. 

Annular  (ring  shaped).  Having  the  appear- 
ance or  form  of  a  ring. 

Aphelion.  The  point  of  the  orbit  of  a  planet 
in  which  it  is  farthest  from  the  Sun. 

Apogee.  The  point  of  an  orbit  in  which  the 
Moon  is  farthest  from  the  Earth.  Applied 
only  to  the  most  distant  part  of  the  Moon's 
orbit. 

Apsis  (pi.  apsides).  The  two  points  of  an 
orbit  which  are  nearest  to,  and  farthest  from, 
the  center  of  motion,  called,  respectively,  the 
lower  and  higher  apsis.  The  line  of  apsides 
is  that  which  joins  these  two  points,  and  so 
forms  the  major  of  an  ecliptic  orbit. 

Azimuth.  The  angular  distance  of  a  point 
of  the  horizon  from  the  North  or  South.  The 


azimuth  of  a  horizontal  line  is  its  deviation 
fiom  the  true  North  and  South  direction.  The 
azimuth  of  the  East  and  West  points  is  90°. 

Centrifugal  (receding  from  the  center).  If 
a  body  be  revolved  about  a  center,  the  tendency 
it  has  when  in  motion  to  fly  off  tangent  to  the 
orbit  in  which  it  revolves,  is  called  centrifugal 
force. 

Centripetal  (tending  toward  the  center).  The 
attractive  force  of  a  body  drawing  another 
body  to  it.  The  gravitating  force  of  one  body 
upon  another. 

Colures. .  .  The  four  principal  meridians  of 
the  celestial  sphere  all  of  which  pass  from  the 
pole,  and  one  of  which  passes  through  the  equi- 
nox, and  one  through  each  solstice.  They  mark 
the  circles  of  0  hr.,  6  hr.,  12  hr.  and  18  hr.  of 
right  ascension,  respectively. 

Conjunction  (a  joining).  The  nearest  ap- 
proach of  two  heavenly  bodies  which  seem  to 
pass  each  other  in  their  course.  They  are 
commonly  considered  as  in  conjunction  when 
they  have  the  same  longtitude.  The  term  is 
applied  especially  in  the  case  of  a  planet  and 
the  Sun.  The  nearest  approach  is  called  su- 
perior conjunction  when  the  planet  is  beyond 
the  Sun;  inferior  when  it  is  between  us  and 
the  Sun. 

Declination.  The  angular  distance  of  a 
heavenly  body  from  the  Equator.  When  North 


of  the  Equator,  it  is  said  to  be  in  North  de- 
clination; otherwise,  in  South  declination. 

Digit.  The  twelfth  part  of  the  diameter  of 
the  Sun  or  Moon,  formerly  used  to  express 
the  magnitude  of  eclipses. 

Dip  of  the  Horizon.  At  sea,  the  depression 
of  the  apparent  horizon  below  the  true  level, 
owing  to  the  height  of  the  observer's  eye  above 
water. 

Direct  Motion.  A  motion  from  West  to  East 
among  the  Stars,  like  that  of  the  Planets  in 
general. 

Ecliptic.  The  apparent  path  of  the  Sun 
among  the  Stars. 

Ecliptic,  plane  of.  [The  great  plane  extend- 
ing through  the  center  of  the  Earth  and  the 
center  of  the  Sun. 

Egress  (a  going  forth).  The  end  of  the  ap- 
parent transit  of  one  body  over  another,  when 
the  former  seems  to  leave  the  latter. 

Equation,  of  Time.  The  difference  between 
the  real  and  the  mean  Sun. 

Equator.  The  great  circle  half  way  between 
the  two  poles  of  the  Earth  or  heavens,  dividing 
the  Earth,  or  celestial  sphere,  into  two  hemi- 
spheres. 

Equinox.  Either  of  the  two  points  in  which 
the  Sun,  in  its  apparent  annual  course  among 
the  Stars,  crosses  the  Equator.  So  called  be- 


—85— 

cause  the  days  and  nights  are  equal  when  the 
Sun  is  at  these  points. 

Hour  Circle  (see  Meridian. 

Inclination  (to  lean  to).  The  inclination  of 
an  orbit  is  the  angle  it  makes  with  a  plane. 
The  angle  made  with  a  perpendicular  to  a 
plane. 

Ingress.  The  commencement  of  the  transit 
of  one  body  over  the  face  of  another. 

Latitude.  The  angular  distance  of  a  heav- 
enly body  from  the  ecliptic,  as  declination  is 
distance  from  the  Equator. 

Longtitude,  celestial.  The  distance  from  the 
first  point  of  Aries,  measured  East  (the  di- 
rection in  which  the  Earth  moves  around  the 
Sun),  on  the  ecliptic;  or  from  the  point  where 
the  Sun  appears  at  the  Vernal  Equinox. 

Lunation.  The  period  from  one  change  of 
the  Moon  to  the  next.  Its  duration  is  29% 
days. 

Mass,  of  a  body.  The  quantity  of  matter 
contained  in  it,  as  measured  by  its  weight  at 
a  given  place.  Mass  differs  from  weight  in 
that  the  latter  is  different  in  different  places, 
even  for  the  same  body,  depending  on  the  in- 
tensity of  gravity,  whereas  the  mass  of  a  body 
is  necessarily  the  same  everywhere. 


—86— 

Meridian,  celestial.  A  great  circle  passing 
from  the  North  to  the  South  Pole,  and  cross- 
ing the  Equator  at  right  angles. 

Nadir.  The  point  of  the  celestial  sphere  di- 
rectly beneath  our  feet,  or  the  direction  ex- 
actly downward. 

Node.  The  point  in  which  an  orbit  inter- 
sects the  ecliptic,  or  other  plane  of  reference. 
Usually  applied  to  the  Moon's  orbit  crossing 
the  ecliptic. 

Nutation.  A  very  small  oscillation  of  the 
direction  of  the  Earth's  axis.  It  arises  from 
the  fact  that  the  forces  which  produce  the  pre- 
cession of  the  equinoxes  do  not  act  uniformly, 
and  may,  therefore,  be  considered  as  the  in- 
equality of  the  precession  arising  from  the  in- 
equality of  the  forces  which  produce  it. 

Oblate.  Applied  to  a  round  body  which  dif- 
fers from  a  sphere  in  being  flattened  at  the 
Poles,  as  in  the  case  of  the  Earth. 

Obiquity  of  the  Ecliptic.  The  inclination  of 
the  plane  of  the  Equator  to  that  of  the  ecliptic, 
which  is  equal  to  half  the  difference  between 
the  greatest  meridian  altitude  of  the  Sun, 
which  occurs  about  June  21,  and  the  least, 
which  occurs  about  December  21,  which  is  23y2 
degrees. 

Opposition.  A  position  of  a  planet  with  ref- 
erence to  the  Sun.  A  planet  is  said  to  be  in 


—87— 

opposition  when  it  is  in  the  opposite  direction 
from  the  Sun.  The  planet  then  arises  at  sun- 
set and  sets  at  sunrise.  A  superior  planet  only 
can  be  in  opposition. 

Orbit.  The  path  described  by  a  Planet 
around  the  Sun,  or  by  a  satellite  around  its 
primary  Planet. 

Parallels.  Imaginary  circles  on  the  Earth, 
or  in  the  heavens,  parallel  to  the  Equator,  and 
having  the  Pole  as  their  center. 

Peri  (near).  A  general  prefix  to  denote  the 
point  at  which  a  body  revolving  in  an  orbit 
comes  nearest  to  its  center  of  motion ;  as,  peri- 
helion, the  point  nearest  the  Sun ;  perigee,  that 
nearest  the  Earth. 

Precession  of  the  Equinoxes.  The  Equator 
crosses  the  ecliptic  at  the  First  Point  of  Aries. 
The  Precession  of  the  Equinoxes  consists  of 
a  backward  movement  of  the  First  Point  as  a 
result  of  which  in  about  26,000  years,  it  will 
have  traveled  entirely  around  the  ecliptic. 

Quadrature.  The  position  of  the  Moon 
when  it  is  90°  from  the  Sun,  and,  therefore, 
in  its  first  or  last  quarter. 

Radius-vector.  A  straight  line  joining  the 
Sun  to  a  heavenly  body. 

Right  Ascension.  A  term  employed  to  lo- 
cate a  celestial  body.  It  is  the  angular  dis- 
tance of  that  body  from  the  First  Point  of 


Aries  as  measured  along  the  celestial  equator 
to  the  east. 

Siderial.  Kelating  to  the  Stars.  Siderial 
time  is  time  measured  by  the  apparent  diurnal 
revolution  of  the  stars.  Each  unit  of  siderial 
time  is  about  l-365th  part  shorter  than  a  unit 
of  mean  time. 

Signs  of  the  Zodiac.  The  twelve  equal  parts 
into  which  the  zodiac  was  divided  by  the  an- 
cient astronomers. 

Solstices  (standing  points  of  the  Sun.) 
Those  points  of  the  ecliptic  where  the  Sun  is 
most  distant  from  the  Equator,  and  through 
which  the  Sun  passes  about  June  21  and  De- 
cember 21.  So  called  because  the  Sun,  having 
then  attained  its  greatest  declination,  ceases 
its  motion  in  declination  and  begins  to  return 
toward  the  Equator.  The  two  solstices  are 
designated  as  those  of  Summer  and  "Winter 
respectively  the  first  being  in  6  hours  and  the 
second  in  18  hours  of  right  ascension. 

Syzygy.  The  points  of  the  Moon's  orbit  in 
which  it  is  either  New  Moon  or  Full  Moon. 
The  line  of  the  Syzygy  is  that  which  passes 
through  these  points,  crossing  the  orbit  of  the 
Moon. 

Transit  (a  passing  across).  The  passage 
of  an  object  across  some  fixed  line,  as  the  me- 
ridian, for  example,  or  between  the  eye  of  an 


—89— 

observer  and  an  apparently  larger  object  be- 
yond, so  that  the  nearer  object  appears  on  the 
face  of  the  more  distant  one. 

Umbra  (a  shadow).  The  darkest  part  of 
the  shadow  of  an  object  where  no  part  of  the 
luminous  object  can  be  seen. 

Vertical,  angle  of.  The  small  angle  by 
which  the  real  direction  of  the  Earth's  center 
from  any  point  on  its  surface  differs  from  that 
which  is  directly  downward,  as  indicated  by 
the  plumb-line. 

Zenith.  The  point  of  the  celestial  sphere 
which  is  directly  overhead. 

Zodiac.  A  belt  encircling  the  heavens  on 
each  side  of  the  ecliptic,  within  which  the 
larger  Planets  always  remain.  Its  breadth  is 
generally  considered  to  be  about  sixteen  de- 
grees— eight  degrees  on  each  side  of  the  elip- 
tic. 


How  to  Set  Up  and  Adjust 
the  Tellurian 


To  set  up  the  Tellurian  there  is  but  one  oper- 
ation: Put  Earth  Arm  (No.  3)  into  socket  at 
(No.  7)  and  fasten  with  Set  Screw  (No.  8). 

To  adjust:  Release  the  Clutch  (No.  12); 
bring  the  Earth  Arm  over  December  21  marked 
on  the  top  of  the  stand.  Eevolve  the  Earth 
and  the  Moon  on  their  common  centers  until 
the  axis  rod  has  its  greatest  inclination  from 
the  Sun.  Fasten  Clutch. 

To  adjust  the  Moon  for  any  year:  With 
Tellurian  adjusted  and  in  gear,  revolve  until 
Earth  Arm  is  over  the  date  of  new  Moon  near 
est  to  January  1.  Eelease  Clutch  and  revolve 
Earth  and  Moon  upon  their  common  centers 
enough  to  bring  the  Moon  Arm  directly  over 
the  Earth  Arm.  This  will  never  require  more 
than  one-half  a  revolution.  Fasten  the  Clutch 
and  the  Tellurian  will  show  all  new  Moon  dates 
for  that  year  or  for  several  years. 

To  adjust  for  Eclipses :  Bring  to  new  Moon 
as  above  directed  on  date  of  a  total  or  annual 
eclipse  of  the  Sun  as  given  by  the  almanac  or 
other  source.  With  the  fingers,  adjust  the 


—91— 

Moon  cam  so  that  the  Moon  arm  will  be  sup- 
ported directly  underneath  one  of  the  neutral 
marks  on  opposite  sides  of  the  cam.  These  are 
to  represent  the  Moon's  nodes.  One  should 
know  whether  it  is  at  the  ascending  or  descend- 
ing node  that  the  eclipse  occurs.  Then  operate 
the  Tellurian  and  all  eclipses  for  that  year  or 
for  a  number  of  years  may  be  foretold. 


How  to  Demonstrate  to  a  Class 

What  the  Axis  of  the 

Earth  Means 


In  the  past  the  teacher  has  used  a  pencil  run 
through  the  center  of  an  apple  or  an  orange. 
The  pencil  represented  the  axis  of  the  earth, 
the  apple  or  orange,  the  earth  revolving  around 
the  axis.  Instead  of  this  obsolete  system, 
demonstrate  with  the  Matlick  Tellurian  as  fol- 
lows :  Simply  draw  the  Long  Pin  (No.  14)  from 
the  top  of  the  Earth  Globe  and  reverse  it,  and 
place  the  part  which  protrudes  from  the  top  of 
the  Earth  Globe  into  the  hole  in  which  the 
Earth  Globe  revolves.  The  teacher  will  find 
that  this  represents  the  axis  of  the  Earth,  and 
by  revolving  the  Long  Arm  (No.  3)  around  the 
Sun  (No.  2)  in  the  usual  manner  the  axis  of 
the  Earth  will  be  represented  as  continually 
pointing  in  the  same  objective  direction  in- 
clined 231/o  degrees  from  a  perpendicular.  In 
this  demonstration,  of  course,  the  Earth  Globe 
is  removed,  also  the  Time  Band  (No.  13). 


14  DAY  USE 

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General  Library 

University  of  California 

Berkeley 


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UNIVERSITY  OF  CALIFORNIA  UBRARY 


